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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 ${\mathbb{C}}{\mathbb{P}}^3$ or the inversion of a minimal surface with planar ends in ${\mathbb{R}}^4$. 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.

53C42Immersions (differential geometry)
53C43Differential geometric aspects of harmonic maps
53A30Conformal differential geometry
Full Text: DOI arXiv
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