Hypersurfaces with nonnegative Ricci curvature in hyperbolic space
Differential Geometry
2017-09-04 v1
Abstract
Based on properties of n-subharmonic functions we show that a complete, noncompact, properly embedded hypersurface with nonnegative Ricci curvature in hyperbolic space has an asymptotic boundary at infinity of at most two points. Moreover, the presence of two points in the asymptotic boundary is a rigidity condition that forces the hypersurface to be an equidistant hypersurface about a geodesic line in hyperbolic space. This gives an affirmative answer to the question raised by Alexander and Currier in 1990.
Keywords
Cite
@article{arxiv.1709.00091,
title = {Hypersurfaces with nonnegative Ricci curvature in hyperbolic space},
author = {Vincent Bonini and Shiguang Ma and Jie Qing},
journal= {arXiv preprint arXiv:1709.00091},
year = {2017}
}
Comments
14 pages