Calculus of Variations and Geometric Measure Theory

A. Michelat - A. Mondino

Quantization of the Willmore Energy in Riemannian Manifolds

created by mondino on 28 Dec 2021



Inserted: 28 dec 2021
Last Updated: 28 dec 2021

Year: 2021


We show that the quantization of energy for Willmore spheres into closed Riemannian manifolds holds provided that the Willmore energy and the area are 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 in a compact domain of the moduli space.