Morse Index Estimates of Min-Max Willmore Surfaces

Abstract

We show that the sum of the Morse indices of the Willmore spheres realising the width of Willmore type sweep-outs is bounded by the number of the parameters of the min-max. As an application, we deduce that among the true Willmore spheres realising the min-max sphere eversion, at most one of them one has index 1, while the others must be stable.

arXiv comment62 pages

References in corpus (4)

• Asymptotic Analysis of Branched Willmore Surfaces
• Minmax Hierarchies and Minimal Surfaces in Manifolds
• Computer-Assisted Proof of the Main Theorem of 'The Classification of Branched Willmore Spheres in the $3$-Sphere and the $4$-Sphere'
• Lower Semi-Continuity of the Index in the Visosity Method for Minimal Surfaces