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Morse Index and Willmore Stability of Minimal Surfaces in Spheres
Author: Release time:2018-05-29 Number of clicks:

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

Speaker: Peng Wang

Affiliation:Tongji University

Time: 2018-5-30 15:00-16:00

Venue: Room 203 Lecture Hall

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 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).



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