Abstract
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
.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
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