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Sequences of Willmore surfaces. (English) Zbl 1151.53056
Summary: We develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore surface either is the twistor projection of a holomorphic curve into $ℂ{ℙ}^{3}$ or the inversion of a minimal surface with planar ends in ${ℝ}^{4}$. These results give a unified explanation of previous work on the characterization of Willmore spheres and Willmore tori with non-trivial normal bundles by various authors.
##### MSC:
 53C42 Immersions (differential geometry) 53C43 Differential geometric aspects of harmonic maps 53A30 Conformal differential geometry
##### References:
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