Classification of branched Willmore spheres
Differential Geometry
2024-07-02 v2
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 -topology of the conformal Gauss map at a branched point is a null straight line.
Cite
@article{arxiv.2306.07965,
title = {Classification of branched Willmore spheres},
author = {Dorian Martino},
journal= {arXiv preprint arXiv:2306.07965},
year = {2024}
}
Comments
13 pages, Added in v2 : Discussion on the notion of branched Willmore surface