Higher Regularity of Weak Limits of Willmore Immersions I

2019/04/09 by Michelat, Alexis, Rivière, Tristan
#35J35 #35J48 #35R01 #49Q10 #53A05 #53A10 #53A30 #53C42 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.04816

Abstract

We obtain in arbitrary codimension a removability result on the order of singularity of weak limits and bubbles of Willmore immersions measured by the second residue. This permits to reduce significantly the number of possible bubbling scenarii. 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 of Willmore immersions.

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