子流形几何与曲率流

In this project, we will invite some famous experts and outstanding young scholars in the field of the geometry of submanifolds and curvature flows to give lectures, teach courses and discuss questions in our seminars. We will focus on several frontier topics, including the geometry and topology of foliations, index theorems on manifolds with boundary, curvature and topology of submanifolds, the Hopf conjecture, isoparametric hypersurfaces and focal submanifolds, isoparametric functions and the geometry of exotic spheres, the Möbius differential geometry, new proof of the Willmore conjecture and the generalized Willmore conjecture for higher dimensional submanifolds; the mean curvature flow, the Ricci flow and the Willmore flow of submanifolds, the extrinsic curvature flows of hypersurfaces, the Schrödinger flow, etc., and the applications of curvature flows in geometry and topology; the Yau conjecture on the first eigenvalue of minimal hypersurfaces in spheres, isoperimetric inequality and related problems, the eigenvalue pinching problem of submanifolds, the estimates of eigenvalues and the evolution of eigenvalues along curvature flows, the existence of bounded harmonic functions, the heat kernel and heat equations on submanifolds; the Chern conjecture on the scalar curvature of minimal hypersurfaces in spheres, the rigidity and geometric inequalities of minimal submanifolds and self-similar submanifolds, etc. By carrying out the project, the research of differential geometry in China will be greatly promoted, a number of internationally influential, original and innovational results will be obtained, and a group of outstanding young talents in mathematics will be trained.

邀请本领域著名专家和优秀青年学者围绕子流形几何与曲率流的前沿专题开展讲学和研讨活动，内容包括：叶层结构的几何与拓扑，带边流形的指标定理，子流形的曲率与拓扑，Hopf猜想，等参超曲面与焦流形，等参函数与怪球面的几何，Möbius微分几何，Willmore猜想的新证明与高维Willmore猜想；子流形的平均曲率流、Ricci流、Willmore流，超曲面的外蕴曲率流，Schrödinger流等，曲率流在几何与拓扑中的应用；球面中极小超曲面第一特征值的丘成桐猜想，等周不等式及相关问题，子流形的特征值拼挤问题，特征值估计及沿曲率流的演化，有界调和函数的存在性问题，子流形的热核与热方程；球面中极小超曲面数量曲率的陈省身猜想，极小子流形、自相似子流形等几类子流形的刚性与几何不等式。通过本项目的实施，有力提升我国微分几何的研究水平，产生一批具有国际影响的原始创新成果，培养出一批年轻的拔尖数学人才。