中科院数学与系统科学研究院

数学研究所

学术报告

非线性分析研讨班

报告人：洪寒（清华大学）

题  目：Stability of capillary surfaces in three-dimensional Riemannian manifolds

时  间：2023.09.27（星期三）10:30-11:20

地  点：思源楼S813

摘  要：In this talk, we will discuss  stability results for noncompact capillary surfaces. A classical result in minimal surface theory by Fischer-Colbrie and Schoen (independently by do Carmo-Peng) says that a stable complete minimal surface in $\mathbb{R}^3$ must be a plane.  We show that, under certain curvature assumptions,  a weakly stable capillary surface in a 3-manifold with boundary has only three possible topological configurations. In particular, we prove that a weakly stable capillary surface in a half-space of $\mathbb{R}^3$ which is minimal or has the contact angle less than or equal to $\pi/2$ must be a half-plane. A natural application of the rigidity result is curvature estimates for capillary surfaces in 3-manifolds. This is a joint work with Artur Saturnino.