When will a minimal surface in S^n be Willmore stable?
主 题: When will a minimal surface in S^n be Willmore stable?
报告人: Peng Wang associate professor (Tongji University)
时 间: 2017-11-03 08:30-10:30
地 点: Room 1479, Sciences Building No. 1
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 S^n. Moreover, the Clifford torus is the only minimal torus (locally) minimizing the Willmore energy in arbitrary codimension. And the equilateral Itoh-Montiel-Ros torus is a constrained-Willmore (local) minimizer, but not a Willmore (local) minimizer. This is a joint work with Prof. Rob Kusner (UMass Amherst).