走向现代数学学术报告 - 高瑞博士（No. 817)

报告题目：Compactness and Existence of Prescribed Mean Curvature Surfaces of Abitrary Codimensions

报告时间：2025年11月6日 14:00

报告地点：东海岸校区-D实209

报 告 人：高瑞 博士（上海交通大学）

邀 请 人：陈优民 博士

报告摘要：Constant Mean Curvature (CMC) and Prescribed Mean Curvature (PMC) surfaces are pivotal in diverse fields including mathematics, physics, and biology. They 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 closed 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 compactness and existence theory for PMC surfaces with arbitrary codimensions, contributing to a supplement of such area. This talk is based on the joint work with Prof. Miaomiao Zhu.

短期课程

摘要：This 4-hour short course, targeting graduate students, early-career researchers in mathematics (differential geometry, PDEs), focuses on basic definitions and variational theory of Constant Mean Curvature (CMC) and Prescribed Mean Curvature (PMC) surfaces of high codimensional case from the mapping perspective. And we will present detailed proofs of our recent advancements in the compactness and existence theory for such surfaces.

时间：2025年11月4日 14:00-16:00，2025年11月5日 15:00-17:00

地点：东海岸校区-D实232

报告人简介：高瑞，上海交通大学博士研究生，主要从事微分几何和几何分析研究，在国际知名期刊CVPDE, JGA, PAMS发表3篇论文，并在多个学术会议上作邀请报告.