2025/05/09 by Prachi Sahjwani, Sahjwani, Prachi
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · doi:10.48550/arxiv.2505.06422
openalex publication_date 2025/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.