Speaker：Hengyu Zhou (Chongqing University)

Time：2021-01-04 14:00

Location：Tencent Meeting ID：996 351 632（No Password）

Abstract:

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.