Morse Index Estimates of Min-Max Willmore Surfaces

2018/08/23 by Alexis Michelat, Michelat, Alexis
Mathematics · #35J35 #35R01 #49Q10 #53A05 #53A10 #53A30 #53C42 #58E15 #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:35J35 #msc:35R01 #msc:49Q10 #msc:53A05 #msc:53A10 #msc:53A30 #msc:53C42 #msc:58E15

paper · pdf · doi:10.48550/arxiv.1808.07700

62 pages

arxiv created 2018/08/23 · openalex publication_date 2018/08/23 · arxiv updated 2018/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact 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'

Related

• On the Index of Willmore spheres
• On the Morse Index of Branched Willmore Spheres in 3-Space
• Morse Index of Willmore spheres in S³
• Willmore Minmax Surfaces and the Cost of the Sphere Eversion
• Morse index and multiplicity of min-max minimal hypersurfaces