A minimal stable vertical planar end in H^2 x R has finite total curvature

Abstract

We prove that a minimal oriented stable annular end in H^2 x R whose asymptotic boundary is contained in two vertical lines has finite total curvature and converges to a vertical plane. Furthermore, if the end is embedded then it is a horizontal graph.

15 pages

Cited by in corpus (1)

• On the structure of hypersurfaces in ${\mathbb{H}}^n\times \mathbb{R}$ with finite strong total curvature