We obtain in arbitrary codimension a removability result on the order of singularity of Willmore surfaces realising the width of Willmore min-max problems on spheres. As a consequence, out of the twelve families of non-planar minimal surfaces in $\mathbb{ R}^3$ of total curvature greater than $-12\pi$, only three of them may occur as conformal images of bubbles in Willmore min-max problems.
Categories: math.AP math.DG