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arXiv · 2306.07965

Classification of branched Willmore spheres

Dorian Martino
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Abstract

Given a branched Willmore immersion from a closed Riemann surface, we show that Bryant's quartic is holomorphic. Consequently, this quartic vanishes when the underlying surface is a sphere and we obtain the full classification of branched Willmore spheres. To do so, we show that the asymptotic expansion in the $C^2$-topology of the conformal Gauss map at a branched point is a null straight line.

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Dorian Martino. 2023-06-13. Classification of branched Willmore spheres. https://arxiv.org/abs/2306.07965

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