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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.