Branched Willmore Spheres

Details Branched Willmore Spheres Branched Willmore Spheres

2011-12-13

arxiv.org/abs/1112.2877v1

Mathematics

Differential Geometry

Scientific paper

In this paper we classify branched Willmore spheres with at most three branch points (including multiplicity), showing that they may be obtained from complete minimal surfaces in $\R ^ 3$ with ends of multiplicity at most three. This extends the classification result of Bryant. We then show that this may be applied to the analysis of singularities of the Willmore flow of non-Willmore spheres with Willmore energy $ \mc {W} (f) \leq 16\pi$.

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