Calculus of Variations and Geometric Measure Theory

S. Borghini - M. Fogagnolo - A. Pinamonti

The equality case in the substatic Heintze-Karcher inequality

created by pinamonti on 09 Jul 2023
modified on 08 Jul 2024


Accepted Paper

Inserted: 9 jul 2023
Last Updated: 8 jul 2024

Journal: ARMA
Year: 2023


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.