Locally constrained curvature flows and geometric inequalities in hyperbolic space

DOI10.1007/s00208-020-02076-4zbMath1495.53100arXiv2002.10643OpenAlexW3085629553WikidataQ115609079 ScholiaQ115609079MaRDI QIDQ2122069

Yingxiang Hu, Yong Wei, Haizhong Li

Publication date: 5 April 2022

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

Full work available at URL: https://arxiv.org/abs/2002.10643

zbMATH Keywords

quermassintegrallocally constrained curvature flowsAlexandrov-Fenchel type inequalities\(h\) convexity\(k\)th (shifted) mean curvature\(k\)th Gauss-Bonnet curvatureBrendle-Guan-Li's flow

Mathematics Subject Classification ID

Global submanifolds (53C40) Mixed volumes and related topics in convex geometry (52A39) Geometric evolution equations (53E99) Flows related to mean curvature (53E10)

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Cites Work

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• An Alexandrov-Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality
• Contracting convex hypersurfaces by curvature
• Inverse curvature flows in hyperbolic space
• Geometric inequalities for hypersurfaces with nonnegative sectional curvature in hyperbolic space
• Four-manifolds with positive curvature operator
• Contraction of convex hypersurfaces in Riemannian spaces
• Quermassintegral preserving curvature flow in hyperbolic space
• Three-manifolds with positive Ricci curvature
• Isoperimetric problems for spacelike domains in generalized Robertson-Walker spaces
• A geometric inequality on hypersurface in hyperbolic space
• Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space
• Hyperbolic Alexandrov-Fenchel quermassintegral inequalities. II
• A Minkowski Inequality for Hypersurfaces in the Anti‐de Sitter‐Schwarzschild Manifold
• A volume-preserving anisotropic mean curvature type flow
• A volume preserving flow and the isoperimetric problem in warped product spaces
• Locally constrained inverse curvature flows
• A Mean Curvature Type Flow in Space Forms
• Curvature Measures, Isoperimetric Type Inequalities and Fully Nonlinear PDEs
• Pinching estimates and motion of hypersurfaces by curvature functions
• The GBC mass for asymptotically hyperbolic manifolds