A Bernstein Type Theorem for Minimal Graphs over Convex Cones

Nick Edelen, Zhehui Wang

Published 2020-08-16Version 1

Given any $n \geq 2$, we show that if $\Omega \subsetneq \mathbb{R}^n$ is an open, convex cone (e.g. a half-space), and $u : \Omega \to \mathbb{R}$ is a solution to the minimal surface equation which agrees with a linear function on $\partial\Omega$, then $u$ must itself be linear.