The equality case in the substatic Heintze-Karcher inequality
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.
19 pages. Comments welcome