English

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

R2 v1 2026-06-28T11:25:31.540Z