Energy quantization for Willmore surfaces with bounded index
Abstract
We prove an energy quantization result for Willmore surfaces with bounded index, whether the underlying Riemann surfaces degenerates in the moduli space or not. To do so, we translate the question on the conformal Gauss map's point of view. In particular, we prove that in a neck or a collar region, the conformal Gauss map converges to a lightlike geodesic in the De Sitter space.
 Publication:

arXiv eprints
 Pub Date:
 May 2023
 DOI:
 10.48550/arXiv.2305.08668
 arXiv:
 arXiv:2305.08668
 Bibcode:
 2023arXiv230508668M
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs
 EPrint:
 50 pages, minor mistake in the statement of the theorem 4.1 corrected. arXiv admin note: text overlap with arXiv:1606.08004 by other authors