The Equality Case in the Substatic Heintze–Karcher Inequality
Abstract We provide a rigidity statement for the equality case of the Heintze–Karcher inequality in substatic manifolds. We apply such a 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.
Authors
- Stefano Borghini (ORCID: https://orcid.org/0000-0002-6505-5876)
- Andrea Pinamonti (ORCID: https://orcid.org/0000-0003-1000-8607)
- Mattia Fogagnolo (ORCID: https://orcid.org/0000-0002-5933-1344)
Institutions
- University of Padua (IT)
- University of Trento (IT)
Publication Details
- Journal
- Archive for Rational Mechanics and Analysis
- Published
- 2024-11-05
- DOI
- https://doi.org/10.1007/s00205-024-02022-7
- Citations
- 5
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 4.88
Funders
- Università degli Studi di Trento