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Differential Geometry Seminar
Differential Geometry Seminar
Existence of Prescribed Mean Curvature Surfaces of Arbitrary Codimensions
Existence of Prescribed Mean Curvature Surfaces of Arbitrary Codimensions
Organizers
Speaker
Rui Gao
Time
Tuesday, November 18, 2025 3:00 PM - 4:00 PM
Venue
A7-201
Online
Zoom 388 528 9728
(BIMSA)
Abstract
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.