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On the Morse index of branched Willmore spheres in 3-space
Calculus of Variations and Partial Differential Equations ( IF 2.1 ) Pub Date : 2021-06-25 , DOI: 10.1007/s00526-021-01985-9
Alexis Michelat

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 (when the latter exists). 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 \(\mathrm {Ind}_{W}(\vec {\Phi })\le n-1\).



中文翻译:

关于 3 空间中分支 Willmore 球体的 Morse 指数

我们开发了一种计算分支威尔摩球的莫尔斯指数的通用方法,并表明莫尔斯指数等于某个矩阵的指数,其维度等于对偶极小曲面的端点数(当后者存在时)。作为推论,我们发现对于所有浸入的Willmore 球体\(\vec {\Phi }:S^2\rightarrow \mathbb {R}^3\)使得\(W(\vec {\Phi })=4 \pi n\),我们有\(\mathrm {Ind}_{W}(\vec {\Phi })\le n-1\)

更新日期:2021-06-25
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