A half-space theorem for ideal Scherk graphs in $M\times \mathbb{R}$

Abstract

We prove a half-space theorem for an ideal Scherk graph $\Sigma \subset M\times \mathbb{R}$ over a polygonal domain $D\subset M,$ where $M$ is a Hadamard surface whose curvature is bounded above by a negative constant. More precisely, we show that a properly immersed minimal surface contained in $D\times \mathbb{R}$ and disjoint from $\Sigma$ is a translate of $\Sigma .$

arXiv commentFinal version. We strengthened the result by removing the assumption of a lower curvature bound on the Hadamard surface

References in corpus (1)

• The half-space property and entire positive minimal graphs in M x R