Inverse curvature flows in Riemannian warped products

Abstract

The long-time existence and umbilicity estimates for compact, graphical solutions to expanding curvature flows are deduced in Riemannian warped products of a real interval with a compact fibre. Notably we do not assume the ambient manifold to be rotationally symmetric, nor the radial curvature to converge, nor a lower bound on the ambient sectional curvature. The inverse speeds are given by powers $p\le 1$ of a curvature function satisfying few common properties.

34 pages. Fixed minor errors and typos. Comments welcome

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Cited by in corpus (7)

• Surfaces expanding by non-concave curvature functions
• Geometric inequalities involving three quantities in warped product manifolds
• Minkowski inequalities and constrained inverse curvature flows in warped spaces
• Stability of the Positive Mass Theorem and Riemannian Penrose Inequality for Asymptotically Hyperbolic Manifolds Foliated by Inverse Mean Curvature Flow
• Sobolev stability of the PMT and RPI using IMCF
• Long Time Existence of IMCF on Metrics Conformal to Warped Product Manifolds
• Inverse Gauss curvature flows with free boundaries in a cone