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

：林龙智（美国University of California Santa Cruz）
：2025-06-23 09:00
：海韵园实验楼S102

报告人：林龙智（美国University of California Santa Cruz）

时  间：2025年6月23日9:00

地  点：海韵园实验楼S102

内容摘要:

In this talk, we present a convexity property of 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 equation. 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 talk is based on a recent joint work with Da Rong Cheng and Xin Zhou.

个人简介：

林龙智，美国加州大学圣克鲁兹分校数学系终身教授，2011年毕业于美国约翰霍普金斯大学，并在美国罗格斯大学进行博士后研究。林龙智教授的主要研究领域包括几何分析和偏微分方程，专注于几何流，如平均曲率流、调和映照流及相关问题。他在多个知名期刊如 Geom. & Topo.、Analysis & PDE、Crelle’s Journal、CAG、JFA等上发表了多篇重要论文。

 

联系人：夏超