欢迎光临!
您现在所在的位置:首页 >> 通知公告 & 学术信息
学术信息
SEMINARS
Morse Index and Willmore Stability of Minimal Surfaces in Spheres (II)
时间  Datetime
2018-04-10 10:00 — 11:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
王鹏教授
单位  Affiliation
同济大学 & 福建师范大学
邀请人  Host
yihu yang
报告摘要  Abstract

We aim at the Willlmore conjecture in higher co-dimension. It is natural to ask whether the Clifford torus is Willmore stable when the co-dimension increases and whether there are other  Willmore stable tori or not.

We answer these problems for minimal surfaces in $S^n$, by showing that the Clifford torus in $S^3$ and the equilateral Itoh--Montiel--Ros torus in $S^5$ are the only Willmore stable minimal tori in arbitrary higher co-dimension. Moreover, the Clifford torus is the only minimal torus (locally) minimizing the Willmore energy in arbitrary higher codimension. And the equilateral Bryant--Itoh--Montiel--Ros torus is a constrained-Willmore (local) minimizer, but not a Willmore (local) minimizer.

We also generalize Urbano's Theorem to minimal tori in $S^4$ by showing that a minimal torus in $S^4$ has index at least $6$ and the equality holds if and only if it is the Clifford torus. This is a joint work with Prof. Rob Kusner (UMass Amherst).