Energy quantization for Willmore surfaces and applications


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.


Yann Bernard

Fakultät für Mathematik, Universität Regensburg, 93040 Regenseburg, Germany

Tristan Rivière

Department of Mathematics, ETH Zentrum, 8092 Zürich, Switzerland