The Dirichlet problem of translating mean curvature equation

：周恒宇
：2021-01-04 14:30
：腾讯会议APP（线上）

报告人：周恒宇（重庆大学）

时间：1月4日14:30

地点：腾讯会议ID：996 351 632（无设置会议密码）

内容摘要:

In this talk we discuss the Dirichlet problem of translating mean curvature equations in Riemannian manifolds. It is from the existence of minimal graphs with prescribed boundary in conformal cones. The main difficulty is the smooth solution does have a uniformly C^0 estimate in Riemannian manifolds. We propose a NCM condition. Roughly speaking, a bounded domain has the NCM assumptions, no closed minimal embedded hypersurface exists in its closure. We construct an area functional corresponding to this Dirichlet problem，establish a generalized solution theory for the solution to such problem. In particular, the generalized solution yields a unique classical solution for any bounded mean convex domain with the NCM assumption and continuous boundary data. We also give examples to show such NCM assumptions could not be removed.

个人简介：

周恒宇，重庆大学副研究员, 博士毕业于纽约城市大学，研究兴趣是几何分析，在极小曲面和与之相关的Plateau的问题方面做出一系列有趣的结果，文章发表在JFA, IMRN，JGA等杂志上。

 

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