The equality case in the substatic Heintze-Karcher inequality

2023/07/09 by Stefano Borghini, Borghini, Stefano, Mattia Fogagnolo +3 · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2307.04253

Abstract

We provide a rigidity statement for the equality case for the Heintze-Karcher inequality in substatic manifolds. We apply such result in the warped product setting to fully remove assumption (H4) in the celebrated Brendle's characterization of constant mean curvature hypersurfaces in warped products.

Cited by

• Variational properties of the total inverse mean curvature in the plane under boundary constraints
• On the geometry and uniqueness of asymptotically locally hyperbolic static vacuum black holes

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