Asymptotic Plateau Problem in H2xR

TL;DR

This paper solves the asymptotic Plateau Problem for area minimizing surfaces in H2xR, identifying boundary curves that bound such surfaces, and explores the differences for minimal surfaces.

Contribution

It provides a comprehensive solution for area minimizing surfaces in H2xR and highlights the differences for minimal surfaces.

Findings

Characterization of boundary curves bounding area minimizing surfaces

Distinct behavior of minimal surfaces compared to area minimizing surfaces

Complete solution to the asymptotic Plateau Problem in H2xR

Abstract

We give a fairly complete solution to the asymptotic Plateau Problem for area minimizing surfaces in H2xR. In particular, we identify the collection of Jordan curves in the asymptotic boundary of H2xR, which bounds an area minimizing surface in H2xR. Furthermore, we study the similar problem for minimal surfaces, and show that the situation is highly different.