Abstract
We consider a family of embedded, mean convex hypersurfaces which evolve by the mean curvature flow. It follows from general results of White that the inscribed radius at each point on the hypersurface is at least \(\frac{c}{H}\), where \(c\) is a positive constant that depends only on the initial data. Andrews recently gave a new proof of that fact using the maximum principle. In this paper, we show that the inscribed radius is at least \(\frac{1}{(1+\delta ) \, H}\) at each point where the curvature is sufficiently large.
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The author was supported in part by the National Science Foundation under Grant DMS-1201924.
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Brendle, S. A sharp bound for the inscribed radius under mean curvature flow. Invent. math. 202, 217–237 (2015). https://doi.org/10.1007/s00222-014-0570-8
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DOI: https://doi.org/10.1007/s00222-014-0570-8