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arXiv · 1606.08004

Energy Quantization of Willmore surfaces at the boundary of the Moduli Space

Paul Laurain·Tristan Rivière
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Abstract

We establish an energy quantization result for sequences of Willmore surfaces when the underlying sequence of Riemann surfaces is degenerating in the moduli space. we notably exhibit a new residue which quantifies the potential loss of energy in collar regions. Thanks to these residues, we also prove compactness of Willmore immersion with bounded conformal class and energy below $12\pi$.

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Paul Laurain, Tristan Rivière. 2016-06-26. Energy Quantization of Willmore surfaces at the boundary of the Moduli Space. https://doi.org/10.1215/00127094-2018-0010

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