A sharp bound for the inscribed radius under mean curvature flow

作者：Brendle Simon^*

来源：Inventiones Mathematicae, 2015, 202(1): 217-237.

DOI：10.1007/s00222-014-0570-8

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 , where 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 at each point where the curvature is sufficiently large.

• 出版日期2015-10