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

Ana Menezes

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

Differential Geometry 2014-12-31 v2

Authors: Ana Menezes

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 $\Sigma.$

Keywords

minimal surfaces isometric immersions surfaces and embeddings

Cite

@article{arxiv.1306.6305,
  title  = {A half-space theorem for ideal Scherk graphs in $M\times\mathbb R$},
  author = {Ana Menezes},
  journal= {arXiv preprint arXiv:1306.6305},
  year   = {2014}
}

Comments

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

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