Asymptotic H-Plateau Problem in Hyperbolic 3-space

Abstract

We show that if a Jordan curve C in the asymptotic sphere contains a smooth point, there is an embedded H-plane in H^3 asymptotic to C for any H in [0,1).

13 pages, 1 figure

References in corpus (3)

• Least Area Planes in Hyperbolic 3-Space are Properly Embedded
• Embeddedness of the solutions to the H-Plateau Problem
• Non-properly Embedded H-Planes in Hyperbolic 3-Space

Cited by in corpus (4)

• Embedded $H$-Planes in Hyperbolic 3-Space
• Asymptotic Plateau Problem in H2xR
• $H$-Surfaces with Arbitrary Topology in Hyperbolic 3-Space
• Minimal Surfaces in ${\mathbb{H}}_2\times \mathbb{R}$: Nonfillable Curves