Volume preserving mean curvature flow of revolution hypersurfaces between two equidistants

DOI10.1007/s00526-011-0408-9zbMath1247.53080arXiv1008.4271OpenAlexW2152259364WikidataQ125288352 ScholiaQ125288352MaRDI QIDQ662833

Esther Cabezas-Rivas, Vicente Miquel

Publication date: 13 February 2012

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.4271

zbMATH Keywords

equidistantshypersurfaces of revolutionvolume preserving mean curvature flow

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

The curve shortening problem associated to a density, The area preserving curve shortening flow with Neumann free boundary conditions, Non-preserved curvature conditions under constrained mean curvature flows, Volume-preserving mean curvature flow for tubes in rank one symmetric spaces of non-compact type, CURVE SHORTENING FLOWS ON ROTATIONAL SURFACES GENERATED BY MONOTONE CONVEX FUNCTIONS, Snapshots of non-local constrained mean curvature-type flows, Type I singularities in the curve shortening flow associated to a density, Fully nonlinear curvature flow of axially symmetric hypersurfaces with boundary conditions, Equifocal submanifolds in a symmetric space and the infinite dimensional geometry, Axially symmetric volume constrained anisotropic mean curvature flow, Global solutions to the volume-preserving mean-curvature flow

Cites Work

• Flow by mean curvature of convex surfaces into spheres
• Existence of maximal surfaces in asymptotically flat spacetimes
• Volume-preserving mean curvature flow of revolution hypersurfaces in a rotationally symmetric space
• The volume-preserving mean curvature flow in Euclidean space
• Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature
• Comparison theorems and hypersurfaces
• A radius sphere theorem
• Volume-preserving mean curvature flow of rotationally symmetric surfaces
• Behaviour of singularities of the rotationally symmetric, volume-preserving mean curvature flow
• Regularity theory for mean curvature flow
• The normalized mean curvature flow for a small bubble in a Riemannian manifold.
• Bounds for the first Dirichlet eigenvalue attained at an infinite family of Riemannian manifolds
• Mixed volume preserving curvature flows
• On a lower bound for the first eigenvalue of the Laplace operator on a riemannian manifold
• The volume preserving mean curvature flow.
• The volume preserving mean curvature flow near spheres
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Volume preserving mean curvature flow in the hyperbolic space
• Self-intersections for the surface diffusion and the volume-preserving mean curvature flow