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The inverse mean curvature flow in warped cylinders of non-positive radial curvature

Scheuer, Julian 2017. The inverse mean curvature flow in warped cylinders of non-positive radial curvature. Advances in Mathematics 306 , pp. 1130-1163. 10.1016/j.aim.2016.11.003

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Abstract

We consider the inverse mean curvature flow in smooth Riemannian manifolds of the form ([R0,∞)×Sn,g¯) with metric g¯=dr2+ϑ2(r)σ and non-positive radial sectional curvature. We prove, that for initial mean-convex graphs over Sn the flow exists for all times and remains a graph over Sn . Under weak further assumptions on the ambient manifold, we prove optimal decay of the gradient and that the flow leaves become umbilic exponentially fast. We prove optimal C2 -estimates in case that the ambient pinching improves.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Elsevier
ISSN: 0001-8708
Date of First Compliant Deposit: 21 April 2020
Date of Acceptance: 2 November 2016
Last Modified: 24 Nov 2020 14:34
URI: http://orca.cf.ac.uk/id/eprint/131155

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