Mean curvature flow with surgery of mean convex surfaces in R3

• 成果类型: Article
• 署名作者: Brendle, Simon; Huisken, Gerhard
• 署名单位: Stanford University; Eberhard Karls University of Tubingen
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0599-3
• 发表日期: 2016
• 页码: 615-654
• 关键词: 2-convex hypersurfaces; SINGULARITIES; sets; EVOLUTION

摘要

We define a notion of mean curvature flow with surgery for two-dimensional surfaces in with positive mean curvature. Our construction relies on the earlier work of Huisken and Sinestrari in the higher dimensional case. One of the main ingredients in the proof is a new estimate for the inscribed radius established by the first author (Invent Math, 2015).