Asymptotic plateau problem in $${\mathbb H}^2\times {\mathbb R}$$ H 2 × R

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.