Abstract
In this paper 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.
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K. Leschke thanks the Department of Mathematics and Statistics at the University of Massachusetts, Amherst, and the Center for Geometry, Analysis, Numerics and Graphics for their support and hospitality.
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Leschke, K., Pedit, F. Sequences of Willmore surfaces. Math. Z. 259, 113–122 (2008). https://doi.org/10.1007/s00209-007-0214-4
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DOI: https://doi.org/10.1007/s00209-007-0214-4