Heintze–Karcher and Jellett‐type theorems in conformally flat spaces

DOI10.1002/mana.202200218WikidataQ122229484 ScholiaQ122229484MaRDI QIDQ6144859

Paulo Alexandre Araújo Sousa, Abdênago Alves de Barros, Unnamed Author

Publication date: 8 January 2024

Published in: Mathematische Nachrichten (Search for Journal in Brave)

zbMATH Keywords

mean curvatureconformally flat spacesstar-shaped hypersurface

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

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• An Alexandrov-Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality
• Constant mean curvature surfaces in warped product manifolds
• An extension of Jellett's theorem
• New examples of constant mean curvature immersions of (2k-1)-spheres into euclidean 2k-space
• Uniqueness results for free boundary minimal hypersurfaces in conformally Euclidean balls and annular domains
• An integral formula and its applications on sub-static manifolds
• A Gibbons-Penrose inequality for surfaces in Schwarzschild spacetime
• A general comparison theorem with applications to volume estimates for submanifolds
• CONSTANT HIGHER-ORDER MEAN CURVATURE HYPERSURFACES IN RIEMANNIAN SPACES
• A Minkowski Inequality for Hypersurfaces in the Anti‐de Sitter‐Schwarzschild Manifold
• Scalar Curvature Functions in a Conformal Class of Metrics and Conformal Transformations
• Isoperimetric inequalities for submanifolds. Jellett-Minkowski's formula revisited

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