Higher Regularity of Weak Limits of Willmore Immersions II

2019/04/22 by Michelat, Alexis, Rivière, Tristan
#35J35 #35R01 #49Q10 #53A05 #53A10 #53A30 #53C42 #58E15 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.09957

Abstract

We obtain in arbitrary codimension a removability result on the order of singularity of Willmore surfaces realising the width of Willmore min-max problems on spheres. As a consequence, out of the twelve families of non-planar minimal surfaces in ℝ³ of total curvature greater than -12π, only three of them may occur as conformal images of bubbles in Willmore min-max problems.

Related

• Higher Regularity of Weak Limits of Willmore Immersions I
• Willmore surfaces in spheres via loop groups III: on minimal surfaces in space forms
• Analysis aspects of Willmore surfaces
• Analysis of Constrained Willmore Surfaces
• Variational Principles for immersed Surfaces with L²-bounded Second\n Fundamental Form