A volume preserving flow and the isoperimetric problem in warped product spaces

DOI10.1090/tran/7661zbMath1421.53067arXiv1609.08238OpenAlexW2963675044WikidataQ129469407 ScholiaQ129469407MaRDI QIDQ5227968

Mu-Tao Wang, Junfang Li, Pengfei Guan

Publication date: 7 August 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.08238

zbMATH Keywords

warped product space

Mathematics Subject Classification ID

Related Items (22)

Locally constrained curvature flows and geometric inequalities in hyperbolic space ⋮ A locally constrained mean curvature type flow with free boundary in a hyperbolic ball ⋮ Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball ⋮ The isoperimetric inequality in steady Ricci solitons ⋮ Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball ⋮ The mean curvature type flow in Lorentzian warped product ⋮ Weighted isoperimetric inequalities in warped product manifolds ⋮ A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms ⋮ On the mean curvature type flow for convex capillary hypersurfaces in the ball ⋮ Hopf type theorems for surfaces in the de Sitter-Schwarzschild and Reissner-Nordstrom manifolds ⋮ Locally constrained inverse mean curvature flow in GRW spacetimes ⋮ A mean curvature type flow with capillary boundary in a unit ball ⋮ Uniqueness of isometric immersions with the same mean curvature ⋮ A volume-preserving anisotropic mean curvature type flow ⋮ The Minkowski inequality in de Sitter space ⋮ Parabolic approaches to curvature equations ⋮ Isoperimetric problems for spacelike domains in generalized Robertson-Walker spaces ⋮ Isoperimetric symmetry breaking: a counterexample to a generalized form of the log-convex density conjecture ⋮ Extrinsic curvature flows and applications ⋮ Locally constrained inverse curvature flows ⋮ Minkowski inequalities and constrained inverse curvature flows in warped spaces ⋮ Stable capillary hypersurfaces supported on a horosphere in the hyperbolic space

Cites Work

• Constant mean curvature surfaces in warped product manifolds
• Minkowski formulae and Alexandrov theorems in spacetime
• The log-convex density conjecture and vertical surface area in warped products
• Flow by mean curvature of convex surfaces into spheres
• Isoperimetric problems on the sphere and on surfaces with density
• Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature
• Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces
• Einstein manifolds
• On the Hessian of a function and the curvature of its graph
• The geometry of photon surfaces
• The volume preserving mean curvature flow.
• A Mean Curvature Type Flow in Space Forms
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