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.

14 pages, and 5 figures. arXiv admin note: substantial text overlap with arXiv:1908.01451

References in corpus (2)

• Asymptotic H-Plateau Problem in Hyperbolic 3-space
• Asymptotic Plateau Problem in H2xR