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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
On the Morse Index of Branched Willmore Spheres in $3$-SpaceMay 14 2019Jun 25 2019We develop a general method to compute the Morse index of branched Willmore spheres and show that the Morse index is equal to the index of certain matrix whose dimension is equal to the number of ends of the dual minimal surface. As a corollary, we find ... 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