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On the Morse Index of Branched Willmore Spheres in $3$-SpaceMay 14 2019We develop a general method to compute the Morse index of branched Willmore spheres and show that for immersions the Morse index is equal to a certain matrix whose dimension is equal to the number of end of the dual minimal surface. As a corollary, we ... More

Higher Regularity of Weak Limits of Willmore Immersions IIApr 22 2019We 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 $\mathbb{R}^3$ ... More

Morse Index Estimates of Min-Max Willmore SurfacesAug 23 2018We show that the sum of the Morse indices of the Willmore spheres realising the width of Willmore type sweep-outs is bounded by the number of the parameters of the min-max. As an application, we deduce that among the true Willmore spheres realising the ... More

Computer-assisted proof of the main theorem of 'The Classification of branched Willmore spheres in the $3$-sphere and the $4$-sphere'Nov 28 2017Dec 04 2017We provide a computer-assisted proof of the holomorphy of the quartic and the octic meromorphic differentials arising in the main theorem 4.11 of our paper 'The Classification of branched Willmore spheres in the $3$-sphere and the $4$-sphere' (arXiv:1706.01405), ... More

Computer-Assisted Proof of the Main Theorem of 'The Classification of Branched Willmore Spheres in the $3$-Sphere and the $4$-Sphere'Nov 28 2017Apr 23 2019We provide a computer-assisted proof of the holomorphy of the quartic and the octic meromorphic differentials arising in the main Theorem 4.11 of our paper 'The Classification of Branched Willmore spheres in the $3$-Sphere and the $4$-Sphere' (arXiv:1706.01405), ... More

The Classification of Branched Willmore Spheres in the $3$-Sphere and the $4$-SphereJun 05 2017Apr 23 2019We extend the classification of Robert Bryant of Willmore spheres in $S^3$ to variational branched Willmore spheres $S^3$ and show that they are inverse stereographic projections of complete minimal surfaces with finite total curvature in $\mathbb{R}^3$ ... More

The Classification of branched Willmore spheres in the $3$-sphere and the $4$-sphereJun 05 2017Nov 28 2017We extend the classification of Robert Bryant of Willmore spheres in $S^3$ to true branched Willmore spheres and show that non-completely umbilic variational branched Willmore spheres in $S^3$ are inverse stereographic projections of complete minimal ... More