Quantization of the Willmore energy in Riemannian manifolds
Abstract
We show that the quantization of energy for Willmore spheres into closed Riemannian manifolds holds provided that the Willmore energy and the area be uniformly bounded. The analogous energy quantization result holds for Willmore surfaces of arbitrary genus, under the additional assumptions that the immersion maps weakly converge to a limiting (possibly branched, weak immersion) map from the same surface, and that the conformal structures stay within a compact domain of the moduli space.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Publication details
- Journal / source
- Advances in Mathematics
- Publisher
- Elsevier BV
- Volume
- 489
- Pages
- 110789–110789
- Publication date
- 23 January 2026
- Language
- EN