Convex hypersurfaces with pinched principal curvatures and flow of convex hypersurfaces by high powers of curvature
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]
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|Source:||Transactions of the American Mathematical Society|
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