Sequences of willmore surfaces

K Leschke
F Pedit, University of Massachusetts - Amherst

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.