SINGULARITY REMOVABILITY AT BRANCH POINTS FOR WILLMORE SURFACES

We consider a branched Willmore surface immersed in R-m >= 3 with square-integrable second fundamental form. We develop around each branch point local asymptotic expansions for the Willmore immersion, its first, and its second derivatives. Our expansions are given in terms of new integer-valued residues which are computed as circulation integrals around the branch point. We deduce explicit "point removability" conditions guaranteeing that the immersion is smooth through the branch point. These conditions are new, even in codimension one.