A sharp bound for the inscribed radius under mean curvature flow

• 成果类型: Article
• 署名作者: Brendle, Simon
• 署名单位: Stanford University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0570-8
• 发表日期: 2015
• 页码: 217-237
• 关键词: minimal tori; SINGULARITIES; SURFACES

摘要

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.