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

Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896 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:	15 Nov 2024 03:15
URI:	https://orca.cardiff.ac.uk/id/eprint/131155

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