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Flow by powers of the Gauss curvature

Andrews, Ben; Guan, Pengfei; Ni, Lei


We prove that convex hypersurfaces in Rⁿ⁺¹ contracting under the flow by any power α > 1/n+2 source of the Gauss curvature converge (after rescaling to fixed volume) to a limit which is a smooth, uniformly convex self-similar contracting solution of the flow. Under additional central symmetry of the initial body we prove that the limit is the round sphere for α≥1.

CollectionsANU Research Publications
Date published: 2016
Type: Journal article
Source: Advances in Mathematics
DOI: 10.1016/j.aim.2016.05.008
Access Rights: Open Access


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