题目：Morse Index and Willmore Stability of Minimal Surfaces in Spheres

报告人：王鹏（同济大学）

报告时间：星期三（5月30日）下午3:00-4:00

地点：英国立博官网中文版203室

摘要：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 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).

报告人简介：王鹏，同济大学数学科学学院教授，2008年博士毕业于北京大学数学科学学院，研究领域为微分几何，主要研究Willmore曲面和极小曲面的几何与分析性质，在《Journal of Differential Geometry》和《Advances in Mathematics》等杂志上发表多篇文章。