Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space
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Publication:2039582
DOI10.4171/JEMS/1059zbMath1482.53116arXiv1805.11776OpenAlexW3149329265WikidataQ115481594 ScholiaQ115481594MaRDI QIDQ2039582
Xuzhong Chen, Yong Wei, Ben Andrews
Publication date: 5 July 2021
Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.11776
hyperbolic spacevolume preserving flowAlexandrov-Fenchel inequalitieshorospherically convex hypersurfaces
Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Geometric evolution equations (53E99) Flows related to mean curvature (53E10)
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Cites Work
- Unnamed Item
- Contracting convex hypersurfaces by curvature
- Moving surfaces by non-concave curvature functions
- The Ricci flow in Riemannian geometry. A complete proof of the differentiable 1/4-pinching sphere theorem
- Hypersurfaces in \(\mathbb H^{n+1}\) and conformally invariant equations: the generalized Christoffel and Nirenberg problems
- Four-manifolds with positive curvature operator
- Smooth functions invariant under the action of a compact Lie group
- Contraction of convex hypersurfaces in Euclidean space
- Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
- The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
- Uniqueness of closed self-similar solutions to \(\sigma_k^\alpha\)-curvature flow
- More mixed volume preserving curvature flows
- Quermassintegral preserving curvature flow in hyperbolic space
- Gauss curvature flow: The fate of the rolling stones
- Three-manifolds with positive Ricci curvature
- Aleksandrov reflection and nonlinear evolution equations. I: The \(n\)-sphere and \(n\)-ball
- Surfaces moving by powers of Gauss curvature
- 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
- Mixed volume preserving curvature flows
- Deforming a hypersurface by its Gauss-Kronecker curvature
- A Priori Estimates for Fully Nonlinear Parabolic Equations
- 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