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 kth mean curvature in hyperbolic space. Furthermore, a uniqueness result for h-convex hypersurfaces satisfying certain curvature equations is obtained.
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