Embedded self-similar shrinkers of genus 0

• 成果类型: Article
• 署名作者: Brendle, Simon
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.183.2.6
• 发表日期: 2016
• 页码: 715-728
• 关键词: minimal-surfaces; Rotational symmetry; EXISTENCE

摘要

We confirm a well-known conjecture that the round sphere is the only compact, embedded self-similar shrinking solution of mean curvature flow in R-3 with genus 0. More generally, we show that the only properly embedded self-similar shrinkers in R-3 with vanishing intersection form are the sphere, the cylinder, and the plane. This answers two questions posed by T. Ilmanen.