Energy quantization for Willmore surfaces and applications

Abstract

We prove a bubble-neck decomposition together with an energy quantization result for sequences of Willmore surfaces into ${\mathbb R}^m$ with uniformly bounded energy and nondegenerating conformal type. We deduce the strong compactness of Willmore closed surfaces of a given genus modulo the Möbius group action, below some energy threshold.

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Authors

Yann Bernard

Fakultät für Mathematik, Universität Regensburg, 93040 Regenseburg, Germany

Tristan Rivière

Department of Mathematics, ETH Zentrum, 8092 Zürich, Switzerland