Energy Quantization for Willmore Surfaces and Applications

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

We prove a bubble-neck decomposition together with an energy quantization
result for sequences of Willmore surfaces into an arbitrary euclidian space
with uniformly bounded energy and non-degenerating conformal type. We deduce
the strong compactness of Willmore closed surfaces of a given genus modulo the
M\"obius group action, below some energy threshold

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