Monotone quantities involving a weighted $σ_k$ integral along inverse curvature flows

preprint2014arXivOpen access

We give a family of monotone quantities along smooth solutions to the inverse curvature flows in Euclidean spaces. We also derive a related geometric inequality for closed hypersurfaces with positive k-th mean curvature.

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Monotone quantities involving a weighted $σ_k$ integral along inverse curvature flows

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Monotone quantities involving a weighted σkσ_kσk​ integral along inverse curvature flows

Abstract

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Monotone quantities involving a weighted $σ_k$ integral along inverse curvature flows