Free boundary minimal surfaces and overdetermined boundary value problems

Published 21 Dec 2018 in math.DG and math.AP | (1812.08943v1)

Abstract: In this paper we establish a connection between free boundary minimal surfaces in a ball in $\mathbb{R}^3$ and free boundary cones arising in a one-phase problem. We prove that a doubly connected minimal surface with free boundary in a ball is a catenoid.

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