Minimal Surfaces in $\mathbb{H}_2\times \mathbb{R}$: Nonfillable Curves

Abstract

We study the asymptotic Plateau problem in $\mathbb{H}_2\times \mathbb{R}$. We give the first examples of non-fillable finite curves with no thin tail in the asymptotic cylinder. Furthermore, we study the fillability question for infinite curves in the asymptotic boundary.