Inverse curvature flows in Riemannian warped products

TL;DR

This paper studies the long-term behavior of expanding inverse curvature flows in general Riemannian warped products, establishing existence and geometric estimates without symmetry or curvature bounds.

Contribution

It proves long-time existence and umbilicity estimates for inverse curvature flows in warped products without assuming symmetry or curvature bounds, broadening previous results.

Findings

Established long-time existence of solutions.

Derived umbilicity estimates for the flows.

Extended analysis to non-symmetric ambient manifolds.

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 $p\leq 1$ of a curvature function satisfying few common properties.