Embedded $H$-Planes in Hyperbolic 3-Space

Abstract

We show that for any C^0 Jordan curve C in the sphere at infinity of H^3, there exists an embedded $H$-plane P_H in H^3 with asymptotic boundary C for any H in (-1,1). As a corollary, we proved that any quasi-Fuchsian hyperbolic 3-manifold M=SxR contains an H-surface S_H in the homotopy class of the core surface S for any H in (-1,1). We also proved that for any C^1 Jordan curve J in the sphere at infinity, there exists a unique minimizing H-plane P_H with asymptotic boundary J for a generic H in (-1,1).

21 pages, 3 figures

References in corpus (3)

• Entropy, minimal surfaces, and negatively curved manifolds
• Asymptotic H-Plateau Problem in Hyperbolic 3-space
• Embeddedness of the solutions to the H-Plateau Problem

Cited by in corpus (2)

• Minimal Surfaces in Hyperbolic 3-manifolds
• Asymptotic Plateau problem for prescribed mean curvature hypersurfaces