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Classification of branched Willmore spheres

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arxiv 2306.07965 v2 pith:X4MJLFFH submitted 2023-06-13 math.DG

Dorian Martino This is my paper · ORCID
classification math.DG
keywords branchedwillmoreclassificationquarticspheressurfaceasymptoticbryant
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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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  1. The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow

    math.DG 2025-06 conditional novelty 8.0 of 10

    Every immersed 2-sphere with Willmore energy at most 12π admits an energy-nonincreasing regular homotopy to a round sphere or to a surface in the explicit family J, giving exactly four regular homotopy classes below 12π.

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