题目：Self-Shrinkers and λ-Hypersurfaces

报告人：成庆明 教授 （重庆理工大学）

地点：致远楼103室

时间：2026年1月6日 15:00-15:50

摘要: In this talk, we consider self-shrinkers of mean curvature flow and λ-hypersurface of weighted volume-preserving mean curvature flow. Since there exists embedded self-shrinkers with genus one which is not isometric to Angenent example on self-shrinkers with genus one, it is known that for embedded self-shrinkers with genus one, one cannot expect to have Lawson type conjecture on embedded minimal surfaces with genus one or Pinkall- Sterling type conjecture on embedded surfaces with constant mean curvature and genus one. We will construct examples of compact and complete non-compact embedded λ-hypersurfaces with different topological types. Thus, we know that for λ-hypersurface, one cannot expect to have Alexandrov type theorem on compact hypersurfaces with constant mean curvature and Brendle type theorem on self-shrinkers and planar domain conjecture on self-shrinkers. Furthermore, geometry of complete λ-hypersurfaces is discussed.

主讲人简介：成庆明，重庆理工大学数学科学研究中心教授, 福冈大学名誉教授，佐贺大学名誉教授。历任日本佐贺大学教授，福冈大学教授，博士生导师。原日本数学会几何组负责人。为中日微分几何的学术交流做出重要贡献。与杨洪苍教授合作解决了国际著名数学家Payne-Polya-Weinberger于1955年提出的关于the buckling problem的特征值万有不等式的难题。进而解决了国际知名学者S.Ashbaugh教授提出的关于the clamped plate problem的特征值万有不等式的问题。国际知名学者S. Ashbaugh教授2017年的论文中，高度评价成庆明教授的研究成果。称他们的成果为在特征值研究领域里实现了“重大突破”(the great strides) 的“杰作”(a tour de force)。成庆明教授在球面中的极小超曲面的Chern猜想，平均曲率流的自收缩子和λ-超曲面等方面也做出重要研究成果。

欢迎各位参加！