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Curvature flow in hyperbolic spaces

Andrews, Ben; Chen, Xuzhong


We study the evolution of compact convex hypersurfaces in hyperbolic space ℍn+1, with normal speed governed by the curvature. We concentrate mostly on the case of surfaces, and show that under a large class of natural flows, any compact initial surface with Gauss curvature greater than 1 produces a solution which converges to a point in finite time, and becomes spherical as the final time is approached. We also consider the higher-dimensional case, and show that under the mean curvature flow a...[Show more]

CollectionsANU Research Publications
Date published: 2017
Type: Journal article
Source: Journal fur Reine und Angewandte Mathematik
DOI: 10.1515/crelle-2014-0121
Access Rights: Open Access


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