# Sequences of willmore surfaces

#### Article comments

This is the pre-published version harvested from arXiv.

http://www.springerlink.com/content/527k428633562648/

#### 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 \mathbbC\mathbbP3CP3 or the inversion of a minimal surface with planar ends in \mathbbR4R4. 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.

#### Suggested Citation

K Leschke and F Pedit. "Sequences of willmore surfaces" Mathematische Zeitschrift 259.1 (2008): 113-122.
Available at: http://works.bepress.com/franz_pedit/19

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