The equality case in the substatic Heintze-Karcher inequality
Differential Geometry
2023-07-11 v1 Analysis of PDEs
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.
Cite
@article{arxiv.2307.04253,
title = {The equality case in the substatic Heintze-Karcher inequality},
author = {Stefano Borghini and Mattia Fogagnolo and Andrea Pinamonti},
journal= {arXiv preprint arXiv:2307.04253},
year = {2023}
}
Comments
19 pages. Comments welcome