The equality case in the substatic Heintze-Karcher inequality
Stefano Borghini, Mattia Fogagnolo, Andrea Pinamonti
TL;DR
This paper establishes a rigidity result for the equality case in the Heintze-Karcher inequality within substatic manifolds and applies it to improve the characterization of constant mean curvature hypersurfaces in warped products.
Contribution
It provides a new rigidity statement for the equality case in the Heintze-Karcher inequality and removes a key assumption in Brendle's characterization of CMC hypersurfaces.
Findings
Rigidity result for the equality case in the Heintze-Karcher inequality.
Application to remove assumption (H4) in Brendle's characterization.
Enhanced understanding of CMC hypersurfaces in warped products.
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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometric and Algebraic Topology