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

Alexis Michelat

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arXiv · 1905.05742

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

Alexis Michelat

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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 $\mathrm{Ind}_{W}(\vec{\Phi})\leq n-1$

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Alexis Michelat. 2019-05-14. On the Morse Index of Branched Willmore Spheres in $3$-Space. https://arxiv.org/abs/1905.05742

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