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arXiv · 1404.2719

Pinching and asymptotical roundness for inverse curvature flows in Euclidean space

Julian Scheuer
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Abstract

We consider inverse curvature flows in the $(n+1)$-dimensional Euclidean space, $n\geq 2,$ expanding by arbitrary negative powers of a 1-homogeneous, monotone curvature function $F$ with some concavity properties. We obtain asymptotical roundness, meaning that circumradius minus inradius of the flow hypersurfaces decays to zero and that the flow becomes close to a flow of spheres.

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Julian Scheuer. 2014-04-10. Pinching and asymptotical roundness for inverse curvature flows in Euclidean space. https://doi.org/10.1007/s12220-015-9627-1

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