On the Morse index of branched Willmore spheres in 3-space
2021 ◽
Vol 60
(4)
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AbstractWe 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 $$\vec {\Phi }:S^2\rightarrow \mathbb {R}^3$$ Φ → : S 2 → R 3 such that $$W(\vec {\Phi })=4\pi n$$ W ( Φ → ) = 4 π n , we have $$\mathrm {Ind}_{W}(\vec {\Phi })\le n-1$$ Ind W ( Φ → ) ≤ n - 1 .
2018 ◽
Vol 58
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pp. 177-201
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Keyword(s):
1976 ◽
Vol 34
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pp. 538-539
1992 ◽
Vol 50
(1)
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pp. 694-695
1990 ◽
Vol 80
(1)
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pp. 1-4
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2019 ◽
Vol 25
(2)
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pp. 256-279
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Keyword(s):
1984 ◽
Vol 4
(4)
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pp. 471-479
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1991 ◽
Vol 30
(01)
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pp. 30-35
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