Energy quantization for Willmore surfaces with bounded index
arXiv:2305.08668
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 light-like geodesic in the De Sitter space.
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