A sharp geometric inequality for closed hypersurfaces in manifolds with asymptotically nonnegative curvature

2023/10/12 by Adam Rudnik, Rudnik, Adam · 2 citations
Mathematics · Physics and Astronomy · #53C24 (Primary) 53C21 (Secondary) #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2310.08245

openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we establish a sharp geometric inequality for closed hypersurfaces in complete noncompact Riemannian manifolds with asymptotically nonnegative curvature using standard comparison methods in Riemannian Geometry. These methods have been applied in a recent work by Xiaodong Wang to greatly simplify the proof of a Willmore-type inequality in complete noncompact Riemannian manifolds of nonnegative Ricci curvature, which was first proved by Agostiniani, Fagagnolo and Mazzieri.

Cited by

• Remark on a geometric inequality for closed hypersurfaces in weighted manifolds
• A Willmore-type inequality for hypersurfaces with asymptotic or integral Ricci curvature bounds

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