On the Morse Index of Branched Willmore Spheres in $3$-Space

Alexis Michelat

On the Morse Index of Branched Willmore Spheres in $3$-Space

Differential Geometry 2019-06-26 v2 Analysis of PDEs

Authors: Alexis Michelat

Abstract

We 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 that for all immersed Willmore spheres $\vec{\Phi}:S^2\rightarrow \mathbb{R}^3$ such that $W(\vec{\Phi})=4\pi n$ , we have $\mathrm{Ind}_{W}(\vec{\Phi})\leq n-1$

Keywords

morse index branched willmore spheres dual minimal surface immersed willmore spheres matrix index

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@article{arxiv.1905.05742,
  title  = {On the Morse Index of Branched Willmore Spheres in $3$-Space},
  author = {Alexis Michelat},
  journal= {arXiv preprint arXiv:1905.05742},
  year   = {2019}
}

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81 pages, extended version

On the Morse Index of Branched Willmore Spheres in $3$-Space

Abstract

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