江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Existence of Prescribed Mean Curvature Surfaces of Abitrary Codimensions.
报告人：高瑞（上海交通大学）
报告时间：2024年12月11日（周三）上午9:00-12:00
报告地点：数学学院A310
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 existence theory for PMC spheres with arbitrary codimensions, contributing to a supplement of such area. This talk is based on the joint work with Prof. Miaomiao Zhu.