Unbounded periodic constant mean curvature graphs on Calibrable Cheeger Serrin domains

TL;DR

This paper characterizes certain Serrin domains as supports of unbounded, periodic constant mean curvature graphs, establishing existence and properties of these graphs and their domains.

Contribution

It introduces a general characterization of Serrin domains supporting unbounded periodic constant mean curvature graphs and proves their calibrability and Cheeger properties.

Findings

Existence of unbounded periodic constant mean curvature graphs supported by Serrin domains.

Serrin domains are shown to be calibrable and Cheeger domains.

Domains solve the 1-Laplacian equation.

Abstract

We prove a general result characterizing a specific class of Serrin domains as supports of unbounded and periodic constant mean curvature graphs. We apply this result to prove the existence of a family of unbounded periodic constant mean curvature graphs, each supported by a Serrin domain and intersecting its boundary orthogonally, up to a translation. We also show that the underlying Serrin domains are calibrable and Cheeger in a suitable sens, and they solve the 1-Laplacian equation.