A note on starshaped hypersurfaces with almost constant mean curvature in space forms

2022/07/10 by Julien Roth, Abhitosh Upadhyay, Roth, Julien +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.2207.04509

9 pages. arXiv admin note: text overlap with arXiv:2206.06727

arxiv created 2022/07/10 · openalex publication_date 2022/07/10 · arxiv updated 2022/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that closed starshaped hypersurfaces of space forms with almost constant mean curvature or almost constant higher order mean curvature are closed to geodesic spheres.

Citations

• On compact embbeded Weingarten hypersurfaces in warped products

Related

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• Constant Mean Curvature Hypersurfaces Condensing to Geodesic Segments and Rays in Riemannian Manifolds
• On compact embbeded Weingarten hypersurfaces in warped products
• Mean curvature flow of star-shaped hypersurfaces
• Quantitative estimates for almost constant mean curvature hypersurfaces