Stability of Minkowski-type inequalities in certain warped product spaces
Differential Geometry
2025-05-13 v1 Analysis of PDEs
Abstract
This paper explores the stability of Minkowski-type inequalities for hypersurfaces in warped product spaces. We establish a stability estimate that bounds the norm of the traceless second fundamental form of the hypersurface in terms of the deficit in the Minkowski inequalities satisfied by the hypersurface. Additionally, we prove the stability of Minkowski inequalities in specific cases of the Reissner-Nordstr\"om Anti-de Sitter (RN-AdS) and Anti-de Sitter Schwarzschild (AdS-Schwarzschild) manifolds, which serve as examples of warped products. We also establish a new rigidity result for locally conformally flat manifolds to understand the stability of these inequalities.
Keywords
Cite
@article{arxiv.2505.06422,
title = {Stability of Minkowski-type inequalities in certain warped product spaces},
author = {Prachi Sahjwani},
journal= {arXiv preprint arXiv:2505.06422},
year = {2025}
}