Locally constrained inverse curvature flows

Abstract

We consider inverse curvature flows in warped product manifolds, which are constrained subject to local terms of lower order, namely the radial coordinate and the generalized support function. Under various assumptions we prove longtime existence and smooth convergence to a coordinate slice. We apply this result to deduce a new Minkowski type inequality in the anti-de-Sitter Schwarzschild manifolds and a weighted isoperimetric type inequality in the hyperbolic space.

The proof of Proposition 7.6 has been minor revised

References in corpus (1)

• Isotropic functions revisited

Cited by in corpus (15)

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• The Minkowski inequality in de Sitter space
• Geometric inequalities involving three quantities in warped product manifolds
• Stability from rigidity via umbilicity
• A constrained mean curvature flow and Alexandrov-Fenchel inequalities
• Minkowski inequalities and constrained inverse curvature flows in warped spaces
• Parabolic approaches to curvature equations
• On the mean curvature type flow for convex capillary hypersurfaces in the ball
• A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms
• On the new weighted geometric inequalities near the sphere in space forms
• A class of weighted isoperimetric inequalities in hyperbolic space
• Alexandrov-Fenchel type inequalities with convex weight in space forms