paper

Classification of branched Willmore spheres

arXiv:2306.07965

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.

13 pages, Added in v2 : Discussion on the notion of branched Willmore surface

Classification of branched Willmore spheres · wovepaper