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小磯 深幸(こいそ みゆき) データ更新日:2018.08.17



主な研究テーマ
幾何学的変分問題の解の大域解析とその応用
キーワード:数学,幾何学,微分幾何学,変分問題,大域解析
2008.10~2019.03.
従事しているプロジェクト研究
A free boundary problem for surfaces with constant mean curvature
2013.01~2014.03, 代表者:Miyuki Koiso, IMI, Kyushu University, Japan
Joint research with Prof. Jaigyoung Choe (Korean Institute for Advanced Study, Korea) on a free boundary problem for surfaces with constant mean curvature..
Geometric variational problems for hypersurfaces
2001.02~2017.03, 代表者:Miyuki Koiso, Kyushu University, Kyushu Univeristy, Japan
Joint research on geometric variational problems for hypersurfaces; Miyuki Koiso (Kyushu U., Japan) and Bennett Palmer (Idaho State U., USA).
Stability and bifurcation for surfaces with constant mean curvature and their generalizations
2009.10~2017.03, 代表者:Miyuki Koiso, Kyushu University, Kyushu University, Japan
Joint research on stability and bifurcation for surfaces with constant mean curvature and their generalizations; Miyuki Koiso (Kyushu U, Japan), Bennett Palmer (Idaho State U., USA), and Paolo Piccione (Univ. of Sao Paulo, Brazil).
平成24年度 九州大学教育研究プログラム・研究拠点形成プロジェクト,研究課題:曲面の変分問題から誘導される発展方程式の幾何解析
2012.04~2013.03, 代表者:小磯深幸, 九州大学マス・」ォア・インダストリ研究所, 九州大学
研究課題:曲面の変分問題から誘導される発展方程式の幾何解析,研究経費:1,150,000円.
材料科学への純粋数学適用に関する研究
2010.06~2013.03, 代表者:若山正人, 九州大学, 九州大学
材料科学への純粋数学適用に関する研究を、九州大学・大学院数理学研究院(2011年4月からは、マス・フォア・インダストリ研究所)の研究者と新日本製鐵株式會社の研究者が協同で行う。.
研究業績
主要著書
主要原著論文
1. Miyuki Koiso, Bennett Palmer, Higher order variations of constant mean curvature surfaces, Calculus of Variations and PDE's, 10.1007/s00526-017-1246-1, 2017.10, We study the third and fourth variation of area for a compact domain in a constant mean curvature surface when there is a Killing field on R^3 whose normal component vanishes on the boundary. Examples are given to show that, in the presence of a zero eigenvalue, the non negativity of the second variation has no implications for the local area minimization of the surface..
2. Miyuki Koiso, Bennett Palmer, Paolo Piccione, Stability and bifurcation for surfaces with constant mean curvature, Journal of the Mathematical Society of Japan, 69, 4, 1519-1554, 2017.10, We give criteria for the existence of smooth bifurcation branches of fixed boundary CMC surfaces in R^3, and we discuss stability/instability issues for the surfaces in bifurcating branches. To illustrate the theory, we discuss an explicit example obtained from a bifurcating branch of fixed boundary unduloids in R^3..
3. Miyuki Koiso, Jaigyoung Choe, Stable capillary hypersurfaces in a wedge, Pacific Journal of Mathematics, 10.2140/pjm.2016.280.1, 280, 1, 1-15, 2015.12, Let $\Sigma$ be a compact immersed stable capillary hypersurface in a wedge bounded by two hyperplanes in $\mathbb R^{n+1}$. Suppose that $\Sigma$ meets those two hyperplanes in constant contact angles $\ge \pi/2$ and is disjoint from the edge of the wedge, and suppose that $\partial\Sigma$ consists of two smooth components with one in each hyperplane of the wedge. It is proved that if $\partial \Sigma$ is embedded for $n=2$, or if each component of $\partial\Sigma$ is convex for $n\geq3$, then $\Sigma$ is part of the sphere. And the same is true for $\Sigma$ in the half-space of $\mathbb R^{n+1}$ with connected boundary $\partial\Sigma$..
4. Miyuki Koiso and Bennett Palmer, Equilibria for anisotropic surface energies with wetting and line tension, Calculus of Variations and Partial Differential Equations, 43, 3, 555-587, 2012.01, We study the stability of surfaces trapped between two parallel planes with free boundary on these planes. The energy functional consists of anisotropic surface energy, wetting energy, and line tension. Equilibrium surfaces are surfaces with constant anisotropic mean curvature. We study the case where the Wulff shape is of ``product form'', that is, its horizontal sections are all homothetic and has a certain symmetry. Such an anisotropic surface energy is a natural generalization of the area of the surface. Especially, we study the stability of parts of anisotropic Delaunay surfaces which arise as equilibrium surfaces. They are surfaces of the same product form of the Wulff shape. We show that, for these surfaces, the stability analysis can be reduced to the case where the surface is axially symmetric and the functional is replaced by an appropriate axially symmetric one. Moreover, we obtain necessary and sufficient conditions for the stability of anisotropic sessile drops..
5. Miyuki Koiso and Bennett Palmer, Anisotropic umbilic points and Hopf's theorem for surfaces with constant anisotropic mean curvature, Indiana University Mathematics Journal, 59, 1, 79-90, 2010.05, 非等方的表面エネルギーは、曲面の各点における法線方向に依存するエネルギー密度の曲面上での総和 (積分) である。与えられたエネルギー密度関数に対し、同じ体積を囲む閉曲面の中での非等方的表面エネルギーの最小解は(平行移動を除き)一意的に存在し、Wulff図形と呼ばれている。より一般に、囲む体積を変えない変分に対する非等方的表面エネルギーの臨界点は、非等方的平均曲率一定曲面となる。本論文では、3次元ユークリッド空間において、Wulff図形が滑らかな狭義凸曲面であるという仮定のもとで、種数0の非等方的平均曲率一定閉曲面は平行移動と相似を除きWulff図形に限ることを証明した。.
6. Miyuki Koiso and Bennett Palmer, Geometry and stability of surfaces with constant anisotropic mean curvature, Indiana University Mathematics Journal, 54, 6, 1817-1852, Vol.54, No.6, pp.1817-1852, 2005.12.
7. Miyuki Koiso, Deformation and stability of surfaces with constant mean curvature, Tohoku Mathematical Journal (2, 54, 1, 145-159, Vol.54, No.1, pp.145-159, 2002.03.
主要総説, 論評, 解説, 書評, 報告書等
主要学会発表等
1. Miyuki Koiso, Uniqueness problem for closed non-smooth hypersurfaces with constant anisotropic mean curvature, International Workshop "Geometry of Submanifolds and Integrable Systems", 2018.03, [URL].
2. Miyuki Koiso, Uniqueness problem for closed non-smooth hypersurfaces with constant anisotropic mean curvature and self-shrinkers of anisotropic mean curvature flow, Workshop "Minimal Surfaces and Related Topics", 2018.01, [URL], We study a variational problem for surfaces in the euclidean space with an anisotropic surface energy. An anisotropic surface energy is the integral of an energy density that depends on the surface normal over the considered surface, which was introduced to model the surface tension of a small crystal. The minimizer of such an energy among all closed surfaces enclosing the same volume is unique and it is (up to rescaling) so-called the Wulff shape. The Wulff shape and equilibrium surfaces of this energy for volume-preserving variations are generalizations of the round sphere and constant mean curvature surfaces, respectively. However, they are not smooth in general. In this talk, we show that, if the energy density function is three times continuously differentiable and convex, then any closed stable equilibrium surface is a rescaling of the Wulff shape. Moreover, we show that, there exists a non-convex energy density function such that there exist closed embedded equilibrium surfaces with genus zero which are not (any homothety of) the Wulff shape. This gives also closed embedded self-similar shrinking solutions with genus zero of the anisotropic mean curvature flow other than the Wulff shape. These concepts and results are naturally generalized to higher dimensions..
3. Miyuki Koiso, Non-uniqueness of closed non-smooth hypersurfaces with constant anisotropic mean curvature and self-shrinkers of anisotropic mean curvature flow, The Third Japanese-Spanish Workshop on Differential Geometry, 2017.09, [URL].
4. Miyuki Koiso, Non-uniqueness of closed non-smooth hypersurfaces with constant anisotropic mean curvature and self-shrinkers of anisotropic mean curvature flow, The Last 60 Years of Mathematical Fluid Mechanics: Longstanding Problems and New Perspectives: In Honor of Professors Robert Finn and Vsevolod Solonnikov, 2017.08, [URL], We study variational problems for surfaces in the euclidean space with an anisotropic surface energy. An anisotropic surface energy is the integral of an energy density which depends on the surface normal over the considered surface. It was first introduced by Gibbs to model the equilibrium shape of a small crystal. If the energy density is constant one, the anisotropic surface energy is the usual area of the surface. The minimizer of an anisotropic surface energy among all closed surfaces enclosing the same volume is unique (up to translations) and it is called the Wulff shape. Equilibrium surfaces of a given anisotropic surface energy functional for volume-preserving variations are called surfaces with constant anisotropic mean curvature (CAMC surfaces). In general, the Wulff shape and CAMC surfaces are not smooth. If the energy density satisfies the so-called convexity condition, the Wulff shape is a smooth convex surface and closed embedded CAMC surfaces are only homotheties of the Wulff shape. In this talk, we show that if the convexity condition is not satisfied, such a uniqueness result is not always true, and also the uniqueness for self-shrinkers with genus zero for anisotropic mean curvature flow does not hold in general. These concepts and results are naturally generalized to higher dimensions..
5. Miyuki Koiso, Geometry of anisotropic surface energy, The 13th annual international conference of KWMS (Korean Women in Mathematical Science), 2017.06, [URL], One of the most important subjects in geometry is variational problem. In this talk, we study variational problems for surfaces in the euclidean space with an anisotropic surface energy. An anisotropic surface energy is the integral of an energy density which depends on the surface normal over the considered surface. It was first introduced by Gibbs to model the equilibrium shape of a small crystal. If the energy density is constant one, the anisotropic surface energy is the usual area of the surface. The minimizer of an anisotropic surface energy among all closed surfaces enclosing the same volume is unique (up to translations) and it is called the Wulff shape. Equilibrium surfaces of a given anisotropic surface energy functional for volume-preserving variations are called surfaces with constant anisotropic mean curvature (CAMC surfaces). In general, the Wulff shape and CAMC surfaces are not smooth. Around each regular (smooth) point, they are graphs of solutions of a second order quasilinear elliptic partial differential equation. These concepts are naturally generalized to higher dimensions, and they have many applications inside and outside mathematics. In this talk, we give fundamental geometric and analytic properties of CAMC hypersurfaces and recent progress in the research on the uniqueness of closed CAMC hypersurfaces with and without singularities..
6. Miyuki Koiso, Stability and bifurcation for surfaces with constant mean curvature, Workshop on "Geometric Inequalities on Riemannian Manifolds", 2016.11, [URL], A surface with constant mean curvature (CMC surface) is an equilibrium surface of the area functional among surfaces which enclose the same volume and satisfy given boundary conditions. A CMC surface is said to be stable if the second variation of the area is nonnegative for all volume-preserving variations. In this talk we first give criteria for stability of CMC surfaces in R^3. We also give a sufficient condition for the existence of smooth bifurcation branches of fixed boundary CMC surfaces, and we discuss stability/instability issues for the surfaces in bifurcating branches. By applying our theory, we determine the stability/instability of some explicit examples of CMC surfaces..
7. 小磯 深幸, Local structure of the space of all triply periodic minimal surfaces in R^3, Workshop "Geometric aspects on capillary problems and related topics", 2015.12, [URL], We study the space of triply periodic minimal surfaces in ${\mathds R}^3$, giving a result on the local rigidity and a result on the existence of bifurcation.
We prove that, near a triply periodic minimal surface with nullity three, the space of triply periodic minimal surfaces consist of a smooth five-parameter family of pairwise non-homothetic surfaces. On the other hand, if there is a smooth one-parameter family of triply periodic minimal surfaces $\{X_t\}_t$ containing $X_0$ where the Morse index jumps by an odd integer, it will be proved the existence of a bifurcating branch issuing from $X_0$. We also apply these results to several known examples..
8. 小磯 深幸, Stable capillary hypersurfaces in a wedge and uniqueness of the minimizer, Asymptotic Problems: Elliptic and Parabolic Issues, 2015.06, [URL], Let $\Sigma$ be a compact immersed stable capillary hypersurface in a wedge bounded by two hyperplanes $\Pi_1$, $\Pi_2$ in $\mathbb R^{n+1}$. Suppose $\Sigma$ meets each $\Pi_i$ in constant contact angle not less than $\pi/2$. We prove that if $\partial \Sigma$ is embedded for $n=2$, or if $\partial\Sigma$ is convex for $n\geq3$, then $\Sigma$ is part of the round sphere..
9. 小磯 深幸, Bifurcation theory for minimal and constant mean curvature surfaces, Conference on Geometry, 2014.03, [URL], We construct general criteria for existence and nonexistence of (
continuous and discrete) bifurcation for minimal and constant mean
curvature surfaces. For continuous bifurcation, we also give a criterion
for stability for each surface in the bifurcation branch. We apply our
general results to several concrete boundary value problems. Especially,
we mention the existence of unknown examples of triply periodic minimal
surfaces in the Euclidean three-space which are close to known examples.
This talk is based on joint work with Bennett Palmer (Idaho State U.,
USA) and Paolo Piccione (University of Sao Paulo, Brazil), and joint
work with Paolo Piccione and Toshihiro Shoda (Saga U., Japan). .
10. 小磯 深幸, Stable capillary hypersurfaces in a wedge and uniqueness of the minimizer, The second Japanese-Spanish workshop on Differential Geometry, 2014.02, [URL], We study a variational problem for immersed hypersurfaces in a wedge bounded by two hyperplanes in $\mathbb R^{n+1}$. The total energy of each hypersurface is the $n$-dimensional surface area and a positive ``wetting energy'' on the supporting hyperplanes, and we impose the $(n+1)$-dimensional volume constraint enclosed by the hypersurfaces. Any stationary hypersurface $\Sigma$ is a hypersurface with constant mean curvature which meets each supporting hyperplane with constant contact angle, and it is said to be stable if the second variation of the energy is nonnegative for all admissible variations. We show that if $\Sigma$ is stable and is disjoint from the edge of the wedge, and if $\partial \Sigma$ is embedded for $n=2$, or if $\partial\Sigma$ is convex for $n\geq3$, then $\Sigma$ is part of the hypersphere. Our results also show that the space of stable solutions is not continuous with respect to the variation of the boundary condition. Moreover, we mention the uniqueness of the minimizer. This is joint work with Jaigyoung Choe (KIAS, Korea)..
11. 小磯 深幸, Geometry of hypersurfaces with constant anisotropic mean curvature, The 2013 Annual Meeting of the Taiwan Mathematical Society, 2013.12, [URL], A surface with constant anisotropic mean curvature (CAMC surface) is a stationary surface of a given anisotropic surface energy functional for volume-preserving variations. For example, minimal surfaces and surfaces with constant mean curvature in the Euclidean space and those in the Lorentz-Minkowski space are regarded as CAMC surfaces for a certain special anisotropic surface energy. The minimizer of an anisotropic surface energy among all closed surfaces enclosing the same volume is called the Wulff shape, and the minimizer among surfaces with free boundary on a given support surface is sometimes called the Winterbottom shape. These concepts can be naturally generalized to higher dimensions, and they have many applications inside and outside mathematics. In this talk, we give fundamental geometric properties of CAMC hypersurfaces and recent progress in the research on the stability of CAMC hypersurfaces with free or fixed boundaries..
12. 小磯 深幸, Free boundary problem for surfaces with constant mean curvature, International Workshop on Special Geometry and Minimal Submanifolds, 2013.08, [URL], We study embedded surfaces of constant mean curvature with free boundary in given supporting planes in the euclidean three-space. We assume that each considered surface meets the supporting planes with constant contact angle. These surfaces are characterized as equilibrium surfaces of the variational problem of which the total energy is the surface area and a wetting energy (that is a weighted area of the domains in the supporting planes bounded by the boundary of the considered surface) with volume constraint. An equilibrium surface is said to be stable if the second variation of the energy is nonnegative for all volume-preserving variations satisfying the boundary condition. We are interested in determining all (stable) solutions. At present in literature, only for some special cases, for example, the supporting planes are either just a single plane or two parallel planes and the wetting energy is nonnegative, all stable solutions are known. We discuss recent progress of this subject and show the space of solutions is not continuous with respect to the boundary condition. .
13. 小磯 深幸, Bernstein-type theorems for surfaces with constant anisotropic mean curvature and CMC surfaces in the Lorentz-Minkowski space, 7th International Meeting on Lorentzian Geometry, 2013.07, [URL], A surface with constant anisotropic mean curvature (CAMC surface) is a
stationary surface of a given anisotropic surface energy functional for
volume-preserving variations. Surfaces with constant mean curvature (CMC
surfaces) in the Lorentz-Minkowski space are regarded as CAMC surfaces
for a certain special anisotropic surface energy. In this talk, we show
that if a complete CAMC surface for a uniformly convex anisotropic
surface energy in the euclidean three-space is a graph of a function in
a whole plane, then it is a plane. Moreover, by using a similar method,
we show that if a spacelike complete CMC surface in the Lorentz-
Minkowski three-space satisfies a certain condition on the order of
divergence of its Gauss map, then it is a plane..
14. 小磯 深幸, Non-convex anisotropic surface energy and zero mean curvature surfaces in the Lorentz-Minkowski space, The 5th OCAMI-TIMS Joint International Workshop on Differential Geometry and Geometric Analysis, 2013.03, [URL], We study stationary surfaces of anisotropic surface energies in the euclidean three-space which are called anisotropic minimal surfaces. Usual minimal surfaces, zero mean curvature spacelike surfaces and timelike surfaces in the Lorenz-Minkowski space are regarded as anisotropic minimal surfaces for certain special axisymmetric anisotropic surface energies. In this talk, for any axisymmetric anisotropic surface energy, we show that, a surface is both a minimal surface and an anisotropic minimal surface if and only if it is a right helicoid. We also construct new examples of anisotropic cyclic minimal surfaces for certain reasonable classes of energy density. Our examples include zero mean curvature timelike surfaces and spacelike surfaces of catenoid-type and Riemann- type. This is a joint work with Atsufumi Honda (Tokyo Institute of Technology). .
15. 小磯 深幸, Geometry of isoperimetric-type problems modeled on interfaces on micrometre scale, Workshop on Geometry of Interfaces and Capillarity, 2012.06, [URL], We study geometry of isoperimetric-type problems modeled on interfaces on micrometre scale among two or three different phases. Our main subject is surfaces with constant (anisotropic) mean curvature with free or fixed boundary. We discuss existence, stability, bifurcation, and topological transition for solutions..
16. 小磯深幸, 等周問題型変分問題の幾何解析, 日本数学会2012年度年会, 2012.03, [URL], 囲む体積を保つ変分に対する面積汎関数の臨界点である平均曲率一定曲面や,その一般化について,安定性(対応する汎関数の極小値を与えるか否か)の判定条件,解の分岐が起こるための十分条件,分岐前後の解の安定性を判定する方法を与え,pitchfork分岐や対称性の崩壊現象が生じることを見る..
17. Miyuki Koiso, Bifurcation and stability for solutions of isoperimetric problems, Workshop "Isoperimetric problems, space-filling, and soap bubble geometry", 2012.03, [URL], A surface with constant mean curvature (CMC surface) is an equilibrium surface of the area functional among surfaces which enclose the same volume with given boundary condition. A CMC surface is said to be stable if the second variation of the area is nonnegative for all volume-preserving variations which satisfy the boundary condition. Choosing the mean curvature H or the volume V enclosed by the surface as parameter, we construct conditions under which a pitchfork bifurcation occurs. We apply our results to several interesting isoperimetric problems with free or fixed boundary conditions in the euclidean space. We also generalize the results to more general variational problems with constraint in higher dimensional spaces..
18. Miyuki Koiso, Pitchfork bifurcation for hypersurfaces with constant mean curvature, The 10th Pacific Rim Geometry Conference 2011 Osaka-Fukuoka, 2011.12, [URL], We consider hypersurfaces with constant mean curvature with given boundary conditions. Choosing the mean curvature $H$ or the volume $V$ enclosed by the hypersurface as parameter, we construct conditions under which a pitchfork bifurcation occurs. We apply our results to isoperimetric problems in the Riemannian products of $S^1$ and simply connected space forms introduced by Pedrosa and Ritor\'e (1999)..
19. Miyuki Koiso, Stability of surfaces with constant anisotropic mean curvature and applications to physical phenomena, III Encontro Paulista de Geometria, 2011.08, [URL], A surface with constant anisotropic mean curvature (CAMC surface) is a critical point of an anisotropic surface energy with volume constraint. CAMC surfaces are a generalization of minimal surfaces and surfaces with constant mean curvature (CMC surfaces). They are not only important in itself but also useful in studying, for example, free boundary problems for CMC and minimal surfaces. A CAMC surface is said to be stable if the second variation of the anisotropic surface energy is nonnegative for all "volume"-preserving variations satisfying given boundary conditions. Useful criteria for stability and existence of bifurcation are given by the eigenvalue problem associated with the second variation of the energy. We will give general methods and applications to several concrete examples which may be interesting from both mathematical and physical points of view..
20. Miyuki Koiso, Stability of hypersurfaces with constant anisotropic mean curvature and
its applications, Spanish-Japanese Workshop on Differential Geometry, 2011.02.
21. Miyuki Koiso, Geometric variational problems and bifurcation theory, 2010 Global KMS International Conference, 2010.10, [URL].
22. Miyuki Koiso, Geometry of hypersurfaces with constant anisotropic mean curvature, Workshop on Hypersurfaces Geometry and Integrable Systems, 2010.08, [URL].
23. Miyuki Koiso, Stability and bifurcation for surfaces with constant mean curvature and their generalizations, 16th School of Differential Geometry, 2010.07, [URL].
24. Miyuki Koiso, Stability and bifurcation for surfaces with constant mean curvature and their generalizations, Oberwolfach workshop ``Progress in Surface Theory'', 2010.05, [URL].
25. Miyuki Koiso, Stability and bifurcation for solutions of isoperimetric type problems, The 2nd TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis, 2010.03, [URL].
26. Miyuki Koiso, Geometric variational problems and bifurcation theory,, The First CREST-SBM International Conference "Random Media", 2010.01, [URL].
27. Miyuki Koiso, A free boundary problem for surfaces with constant anisotropic mean curvature, CONFERENCE Differential Geometry, 2008.06, [URL].
28. Miyuki Koiso, A free boundary problem for surfaces with constant anisotropic mean curvature, The 3rd Geometry Conference for Friendship of Japan and China , 2008.01, [URL].
その他の優れた研究業績
2011.03, 連続講義「曲面の変分問題 --- 極小曲面論入門 --- I, II」(さきがけ数学塾「変分法入門〜幾何学と解析学の橋渡し。そして応用へ〜」2011年3月7日(月)〜3月9日(水),JST三番町ビル1階会議室(東京都),主催:独立行政法人科学技術振興機構 戦略的創造研究推進事業 さきがけ「数学と諸分野の協働によるブレークスルーの探索」研究領域).
学会活動
所属学会名
形の科学会
日本数学教育学会
日本数学会
学協会役員等への就任
2013.09~2017.08, 京都大学数理解析研究所, 専門委員.
2015.03~2017.02, 日本数学会, 全国区代議員.
2013.09~2017.08, 京都大学数理解析研究所, 運営委員.
2013.03~2014.02, 日本数学会, 全国区代議員.
2009.04~2017.05, 日本数学会, 理事.
2011.03~2012.02, 日本数学会, 評議員.
2008.03~2010.02, 日本数学会, 評議員.
2007.04~2008.03, 日本数学会, 代議員.
2006.08~2020.09, 日本学術会議, 連携会員.
学会大会・会議・シンポジウム等における役割
2015.08.10~2015.09.10, The 8th International Congress on Industrial and Applied Mathematics, 座長(Chairmanship).
2013.03.20~2013.03.23, 日本数学会2013年度年会, 座長(Chairmanship).
2013.03.25~2013.03.27, The 5th OCAMI-TIMS Joint International Workshop on Differential Geometry and Geometric Analysis, 座長(Chairmanship).
2013.01.21~2013.01.25, The 7th KIAS Winter School on Differential Geometry, 座長(Chairmanship).
2012.10.22~2012.10.26, Forum "Math-for-Industry" 2012 "Information Recovery and Discovery" 2012, 座長(Chairmanship).
2015.09.25~2015.09.27, MEIS2015 : Mathematical Progress in Expressive Image Synthesis, Program Committee のメンバー.
2015.09.23~2015.09.26, 幾何学阿蘇研究集会, 世話人.
2015.08.27~2015.08.30, 第62回幾何学シンポジウム, 組織委員.
2014.08.23~2014.08.26, 第61回幾何学シンポジウム, 組織委員.
2014.11.12~2014.11.14, MEIS2014, プログラム委員.
2014.09.17~2014.09.20, 幾何学阿蘇研究集会, 世話人.
2013.09.09~2013.09.12, 幾何学阿蘇研究集会, 世話人.
2012.09.22~2012.09.25, 幾何学阿蘇研究集会, 世話人.
2012.09.17~2012.09.17, MSJ-KMS Joint Meeting 2012 (日韓数学会合同会議2012), 組織委員.
2012.08.27~2012.08.30, 第59回幾何学シンポジウム, 組織委員.
2012.02.20~2012.02.22, 第6回 福岡・札幌幾何学セミナー, 主催.
2011.12.01~2011.12.09, The 10th Pacific Rim Geometry Conference 2011 Osaka-Fukuoka, 組織委員,ParII代表.
2011.08.21~2011.08.24, 幾何学阿蘇研究集会, 世話人.
2010.08.29~2010.09.01, 幾何学阿蘇研究集会, 世話人.
2009.06.30~2009.07.02, Conference “Variational Problems for Curves and Surfaces and Related Topics”, 主催.
学会誌・雑誌・著書の編集への参加状況
2009.04~2010.03, 日本数学会「数学通信」, 国内, 編集委員.
2008.04~2009.03, 日本数学会「数学通信」, 国内, 編集委員.
学術論文等の審査
年度 外国語雑誌査読論文数 日本語雑誌査読論文数 国際会議録査読論文数 国内会議録査読論文数 合計
2015年度
2014年度
2013年度
2012年度
2011年度
2010年度
その他の研究活動
海外渡航状況, 海外での教育研究歴
University of Granada, Spain, 2015.12~2015.12.
China National Convention Center, China, 2015.08~2015.08.
Lithuanian Academy of Sciences, Vilnius Jesuit Gymnasium, Lithuania, 2015.05~2015.06.
釜山大学, Korea, 2014.11~2014.11.
COEX, Korea, 2014.08~2014.08.
Galatasaray University, Turkey, 2014.03~2014.03.
National Sun Yat-sen University, Taiwan, 2013.12~2013.12.
University of Sao Paulo, Brazil, 2013.07~2013.07.
Korean Institute for Advanced Study, High 1 Resort, Korea, 2013.01~2013.01.
University of Granada, Spain, 2012.06~2012.06.
International Center for Mathematical Sciences, Edinburgh, UnitedKingdom, 2012.03~2012.03.
Tsinghua University, Beijing, China, 2011.09~2011.09.
サンパウロ大学, Brazil, 2011.08~2011.08.
グラナダ大学, Spain, 2011.02~2011.02.
POSTECH, Korea, 2010.10~2010.10.
Hyderabad, India, 2010.08~2010.08.
サンパウロ大学, Brazil, 2010.07~2010.07.
Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany, 2010.04~2010.05.
National Taiwan University, Taiwan, 2010.03~2010.03.
Korea Institute for Advanced Study, Korea, 2009.11~2009.11.
Murcia大学, Spain, 2009.03~2009.03.
Tsinghua University, China, 2008.09~2008.09.
Banach Center at the Mathematical Conference Center Bedlewo, Poland, 2008.06~2008.06.
Idaho State University, UnitedStatesofAmerica, 2008.03~2008.03.
University of Granada, Spain, 1991.09~1991.09.
Universoty of Warwick, UnitedKingdom, 1990.03~1990.03.
Max-Planck-Institute fur Mathematik, Germany, 1986.10~1988.09.
外国人研究者等の受入れ状況
2015.03~2015.04, 2週間以上1ヶ月未満, University of Sao Paulo, Italy, 日本学術振興会.
2013.12~2014.02, 1ヶ月以上, University of Sao Paulo, Italy, 日本学術振興会.
2012.01~2012.03, 1ヶ月以上, University of Sao Paulo, Brazil, 学内資金.
2012.02~2012.02, 2週間未満, サンパウロ大学, Italy, 科学技術振興機構.
2012.02~2012.02, 2週間未満, Idaho State University, UnitedStatesofAmerica, 科学技術振興機構.
2011.11~2011.12, 2週間未満, University of Notre Dame, Brazil, 学内資金.
2011.11~2011.12, 2週間未満, Sookmyung Women's University, Korea, 科学技術振興機構.
2011.11~2011.12, 2週間以上1ヶ月未満, サンパウロ大学, Italy, 科学技術振興機構.
2011.11~2011.12, 2週間未満, Idaho State University, Japan, 科学技術振興機構.
2011.12~2011.12, 2週間未満, University of Toledo, UnitedStatesofAmerica, 科学技術振興機構.
2011.11~2011.12, 2週間未満, 南開大学, China, 科学技術振興機構.
2011.11~2011.12, 2週間未満, Georgia Institute of Technology, UnitedStatesofAmerica, 科学技術振興機構.
2011.11~2012.12, 2週間未満, 韓国高等研究所(KIAS), Korea, 科学技術振興機構.
2011.01~2011.01, 2週間以上1ヶ月未満, 湖北大学, China, 科学技術振興機構.
2009.12~2009.12, 2週間未満, Idaho State University, UnitedStatesofAmerica, 日本学術振興会.
2009.12~2009.12, 2週間未満, Seoul National University, Korea, 日本学術振興会.
2009.06~2009.07, 2週間以上1ヶ月未満, サンパウロ大学, Italy, 科学技術振興機構.
2009.06~2009.07, 2週間未満, University of Pennsylvania, UnitedStatesofAmerica, 科学技術振興機構.
2009.06~2009.07, 2週間未満, Korea Institute for Advanced Study, Korea, 科学技術振興機構.
2009.05~2009.07, 1ヶ月以上, Idaho State Universityu, UnitedStatesofAmerica, 科学技術振興機構.
2008.10~2008.12, 1ヶ月以上, Idaho State University, UnitedStatesofAmerica, 日本学術振興会.
2008.01~2008.01, 2週間未満, Tsinghua大学, China, 科学技術振興機構.
研究資金
科学研究費補助金の採択状況(文部科学省、日本学術振興会)
2014年度~2018年度, 基盤研究(A), 分担, 特異点をもつ曲線・曲面・超曲面の微分幾何学的研究の推進.
2014年度~2016年度, 基盤研究(C), 分担, 変分原理に基づいた界面張力の概念の普遍化と測定への応用.
2014年度~2016年度, 挑戦的萌芽研究, 代表, 非正則非等方的平均曲率一定超曲面及び超曲面群の研究の新展開.
2013年度~2016年度, 基盤研究(B), 代表, 曲面の変分問題の幾何解析における新しい方法の探求.
2010年度~2012年度, 挑戦的萌芽研究, 代表, 周期的極小曲面、平均曲率一定曲面の安定性と分岐に関する研究、及び、他分野への応用.
2007年度~2009年度, 基盤研究(C), 代表, 幾何学的変分問題の解の安定性と大域的性質に関する研究.
日本学術振興会への採択状況(科学研究費補助金以外)
2018年度~2018年度, 二国間交流, 代表, 幾何学的視点からの形状形成.
2017年度~2017年度, 平成29年度日本学術振興会外国人研究者招へい事業・外国人招へい研究者(短期), 代表, 曲面に対する変分問題,特に自由境界問題の研究と他分野への応用.
2016年度~2016年度, 平成28年度日本学術振興会外国人研究者招へい事業・外国人招へい研究者(短期), 代表, リーマン多様体及び擬リーマン多様体における幾何学的変分問題の解の幾何解析.
2013年度~2013年度, 外国人招へい研究者(短期), 代表, 群作用で不変な汎関数に対する陰関数定理と臨界点の分岐,幾何学的変分問題への応用.
2008年度~2008年度, 外国人招へい研究者(短期), 代表, 曲面に関する変分問題の解の幾何と大域解析,及び,その一般相対性理論への応用.
競争的資金(受託研究を含む)の採択状況
2008年度~2011年度, 戦略的創造研究推進事業 (文部科学省), 代表, 「数学と諸分野の協働によるブレークスルーの探索」領域 さきがけ
幾何学的変分問題の解の大域解析とその応用
.
学内資金・基金等への採択状況
2013年度~2013年度, 平成25年度 九州大学教育研究プログラム・研究拠点形成プロジェクト, 代表, 非正則非等方的平均曲率一定曲面の研究のための新しい方法の探求と他分野への応用.
2012年度~2012年度, 平成24年度 九州大学教育研究プログラム・研究拠点形成プロジェクト, 代表, 曲面の変分問題から誘導される発展方程式の幾何解析.

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