Energy convexity and uniformity of H-surface flow in two dimensions
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：Longzhi Lin (University of California Santa Cruz)
： 2025-06-23 09:00
：Conference Room S102 at Experiment Building at Haiyun Campus
Speaker：Longzhi Lin (University of California Santa Cruz)
Time：2025-6-23 9:00
Location：Conference Room S102 at Experiment Building at Haiyun Campus
Abstract:
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.
