子流形几何与曲率流

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若干前沿专题开展交流和研讨活动，研究和交流内容包括：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，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，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流等及其在几何与物理学中的应用；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，期望能产生一批有质量的新成果，并在促进培养出年轻的几何学人才方面做出贡献，以进一步提升我国微分几何的研究水平。

In this project, we will invite some famous experts and outstanding young scholars in the study field of geometry of submanifolds and curvature flows to give lectures, mini-courses and discussion of questions in our seminars. We will focus on several frontier topics, including the geometry and topology on foliations, index theorems on manifolds with boundary, curvature and topology of submanifolds, 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, Schrödinger flows, 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. We hope that, by carrying out the project, a number of new and iinfluential results will be obtained and a group of outstanding young talents in geometry will be trained, and the research level of differential geometry in China will be greatly promoted.