Quermassintegral preserving curvature flow in hyperbolic space

DOI10.1007/s00039-018-0456-9zbMath1401.53047arXiv1708.09583OpenAlexW3098373012WikidataQ129467786 ScholiaQ129467786MaRDI QIDQ1794364

Yong Wei, Ben Andrews

Publication date: 15 October 2018

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.09583

zbMATH Keywords

hyperbolic spaceAlexandrov reflectionquermassintegral preserving flow

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Integral geometry (53C65) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

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Cites Work

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• Contracting convex hypersurfaces by curvature
• Convex hypersurfaces evolving by volume preserving curvature flows
• Volume-preserving flow by powers of the \(m\)th mean curvature
• Total curvatures of convex hypersurfaces in hyperbolic space
• Contraction of convex hypersurfaces in Euclidean space
• The mixed volume preserving mean curvature flow
• Motion of hypersurfaces by Gauss curvature
• Comparison theorems on convex hypersurfaces in Hadamard manifolds
• Volume-preserving nonhomogeneous mean curvature flow of convex hypersurfaces
• Volume-preserving flow by powers of the \(m\text{-th}\) mean curvature in the hyperbolic space
• More mixed volume preserving curvature flows
• Three-manifolds with positive Ricci curvature
• Volume preserving curvature flows in Lorentzian manifolds
• Curvature flow in hyperbolic spaces
• Volume preserving non-homogeneous mean curvature flow in hyperbolic space
• 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
• Convexity estimates for hypersurfaces moving by convex curvature functions
• The surface area preserving mean curvature flow
• Mixed volume preserving curvature flows
• Deforming a hypersurface by its Gauss-Kronecker curvature
• The volume preserving mean curvature flow.
• Volume preserving anisotropic mean curvature flow
• A Mean Curvature Type Flow in Space Forms
• Pinching estimates and motion of hypersurfaces by curvature functions
• Volume preserving mean curvature flow in the hyperbolic space
• Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces