Stability of Minkowski-type inequalities in certain warped product spaces

Sahjwani, Prachi 2025. Stability of Minkowski-type inequalities in certain warped product spaces. [Online]. Cornell University. Available at: https://doi.org/10.48550/arXiv.2505.06422

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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-Nordström 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.

Item Type:	Website Content
Date Type:	Published Online
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Cornell University
ISSN:	2331-8422
Date of Acceptance:	9 May 2025
Last Modified:	17 Sep 2025 15:45
URI:	https://orca.cardiff.ac.uk/id/eprint/181085

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