Energy Quantization of Willmore surfaces at the boundary of the Moduli Space
Differential Geometry
2018-11-14 v2 Analysis of PDEs
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 .
Keywords
Cite
@article{arxiv.1606.08004,
title = {Energy Quantization of Willmore surfaces at the boundary of the Moduli Space},
author = {Paul Laurain and Tristan Rivière},
journal= {arXiv preprint arXiv:1606.08004},
year = {2018}
}