Minimal surfaces with limit ends in H^2 x R

TL;DR

This paper constructs new examples of properly embedded minimal surfaces in hyperbolic space cross real line, featuring multiple limit ends and vertical bi-graph structures, expanding the known landscape of minimal surface configurations.

Contribution

It introduces a method to construct minimal surfaces with arbitrary numbers of limit ends and vertical planar ends in H^2 x R, including countably infinite limit ends.

Findings

Existence of minimal surfaces with m limit ends for any m > 0

Construction of surfaces with infinitely many limit ends

All examples are vertical bi-graphs

Abstract

For any m > 0, we construct properly embedded minimal surfaces in H^2 x R with genus zero, infinitely many vertical planar ends and m limit ends. We also provide examples with an infinite countable number of limit ends. All these examples are vertical bi-graphs.