题目：Willmore Stability and Morse Index of Minimal Surfaces in Spheres
报告人：王鹏（教授，福建师范大学）
时间：2018年10月26日（周五）下午16:00-17:00
地点：数学院二楼203报告厅
摘要：We aim at the Willlmore conjecture in higher co-dimension. Urbano's index Theorem on Clifford torus plays an important role in Marques and Neves's proof of Willmore conjecture in S^3. We generalize Urbano 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.
It is also 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 tori in S^n, by showing that the Clifford torus in S^3 and the equilateral Bryant-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 co-dimension. And the equilateral (Bryant-Itoh-Montiel-Ros) torus is a (local) constrained-Willmore minimizer, but not a (local) Willmore minimizer.
This is a joint work with Prof. Rob Kusner (UMass Amherst).
