报告人：林龙智（UC Santa Cruz)

时间：7月5日，15:30-16:30

地点：2205

题目: Energy convexity and uniformity of H-surface flow in two dimensions

摘要: In this talk, we will first survey energy convexity and quantitative uniqueness results for weakly harmonic maps and various biharmonic maps. We then present a new convexity property for the energy functional for surfaces of prescribed mean curvature (also known as H-surfaces) in R^3 with prescribed Dirichlet boundary data, yielding a quantitative uniqueness result for solutions to the H-surface system of equations. We will also discuss an energy convexity property along the heat flow for H-surfaces in R^3, assuming only that the initial Dirichlet energy is sufficiently small, leading to a new theorem on the existence of weak solutions, long-time existence, and uniform convergence of the flow to a solution of the H-surface system with prescribed Dirichlet boundary conditions. This new work is joint with Da Rong Cheng (U Miami) and Xin Zhou (Cornell).