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Existence of Prescribed Mean Curvature Surfaces of Arbitrary Codimensions

组织者

深谷賢治 , 杨琳 , 塞巴斯蒂安·赫勒 , 河井公大朗

演讲者

Rui Gao

时间

2025年11月18日 15:00 至 16:00

地点

A7-201

线上

Zoom 388 528 9728 (BIMSA)

摘要

Constant Mean Curvature (CMC) and Prescribed Mean Curvature (PMC) surfaces arise naturally in partitioning problems, isoperimetric problems, general relativity, two-phase interface problems, tissue growth etc. Despite the well-established existence theory for CMC and PMC hypersurfaces, constructing surfaces with prescribed mean curvature vector, admitting prescribed topology and controlled Morse index in general $n$-dimensional compact Riemannian manifold remains elusive. In this talk, we will outline our recent advancements in the min-max construction for PMC surfaces with arbitrary codimensions in both closed and free boundary setting. This talk is based on the joint work with Prof. Miaomiao Zhu.