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arXiv · 1712.09521

Inverse curvature flows in Riemannian warped products

Julian Scheuer
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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.

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Julian Scheuer. 2018-01-24. Inverse curvature flows in Riemannian warped products. https://doi.org/10.1016/j.jfa.2018.08.021

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