Abstract

Abstract:

We prove that for the mean curvature flow of two-convex hypersurfaces the intrinsic diameter stays uniformly controlled as one approaches the first singular time. We also derive sharp $L^{n-1}$-estimates for the regularity scale of the level set flow with two-convex initial data. The results, which seem new even in the most classical case of mean convex surfaces evolving by mean curvature flow in $\Bbb{R}^3$, are ultimately a consequence of the Lojasiewicz inequality from Colding-Minicozzi.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1877-1896
Launched on MUSE
2020-11-11
Open Access
No
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