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Convex hypersurfaces with pinched principal curvatures and flow of convex hypersurfaces by high powers of curvature

Andrews, Ben; McCoy, James


We consider convex hypersurfaces for which the ratio of principal curvatures at each point is bounded by a function of the maximum principal curvature with limit 1 at infinity. We prove that the ratio of the circumradius to the inradius is bounded by a function of the circumradius with limit 1 at zero. We apply this result to the motion of hypersurfaces by arbitrary speeds which are smooth homogeneous functions of the principal curvatures of degree greater than one. For smooth, strictly...[Show more]

CollectionsANU Research Publications
Date published: 2012-07
Type: Journal article
Source: Transactions of the American Mathematical Society
DOI: 10.1090/S0002-9947-2012-05375-X


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