A Heintze-Karcher type inequality in hyperbolic space

Abstract

In this paper, we prove a new Heintze-Karcher type inequality for shifted mean convex hypersurfaces in hyperbolic space. As applications, we prove an Alexandrov type theorem for closed embedded hypersurfaces with constant shifted $k$th mean curvature in hyperbolic space. Furthermore, a uniqueness result for $h$-convex hypersurfaces satisfying certain curvature equations is obtained.

arXiv comment15 pages. All comments are welcome

References in corpus (4)

• Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space
• Locally constrained curvature flows and geometric inequalities in hyperbolic space
• Quermassintegral preserving curvature flow in Hyperbolic space
• Shifted inverse curvature flows in hyperbolic space