Energy quantization for Willmore surfaces and applications

By Yann Bernard, T. Rivière. 2011

83 citations recorded by the source corpus.

We prove a bubble-neck decomposition together with an energy quantization result for sequences of Willmore surfaces into R m with uniformly bounded energy and nondegenerating conformal type. We deduce the strong compactness of Willmore closed surfaces of a given genus modulo

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/aad85040d3fd7c14b431cf62c0cd474478a36d60

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In Applied Mathematics

1. T. Rivière
2. Armin Schikorra
3. Michael Struwe
4. Katarzyna Mazowiecka
5. Yann Bernard
6. L. Martinazzi
7. Francesca Da Lio
8. M. Giaquinta

In Geometry and Topology

1. T. Rivière

Citations in the corpus

• Lipschitz conformal immersions from degenerating Riemann surfaces with L2-bounded second fundamental forms (2013, background): “This result plays a crucial role in [3] for proving the compactness of Willmore surfaces below min18 ; ! g o modulo the action of conformal diffeomorphisms (see [3, Theorem I.”