Non-simply connected minimal planar domains in H^2 x R

TL;DR

This paper demonstrates that any non-simply connected planar domain can be properly embedded as a minimal surface in H^2 x R, using conjugate surface techniques from Jenkins-Serrin graphs.

Contribution

It introduces a method to embed all non-simply connected planar domains minimally in H^2 x R, expanding the class of known minimal surfaces in this space.

Findings

Constructed explicit examples of non-simply connected minimal surfaces

Used conjugate surface techniques from Jenkins-Serrin graphs

Proved proper embedding of these surfaces in H^2 x R

Abstract

We prove that any non-simply connected planar domain can be properly and minimally embedded in H^2 x R. The examples that we produce are vertical bi-graphs, and they are obtained from the conjugate surface of a Jenkins-Serrin graph.