Constant mean curvature surfaces with boundary on a sphere
作者:
Highlights:
•
摘要
In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere with a constant angle. We study under what geometric conditions the surface must be spherical. Our results apply in many scenarios in physics where in absence of gravity a liquid drop is deposited on a round solid ball and the air–liquid interface is a critical point for area under all variations that preserve the enclosed volume.
论文关键词:Mean curvature,Alexandrov method,maximum principle
论文评审过程:Available online 6 July 2013.
论文官网地址:https://doi.org/10.1016/j.amc.2013.06.031