Energy Quantization of Willmore surfaces at the boundary of the Moduli Space

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 $12\pi$.

References in corpus (3)

• Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic Maps
• Conformally Invariant Variational Problems
• Energy Identity for Stationary Yang Mills

Cited by in corpus (8)

• Minimal Bubbling for Willmore Surfaces
• Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature
• Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications
• Higher Regularity of Weak Limits of Willmore Immersions I
• Energy quantization for Willmore surfaces with bounded index
• Classification of branched Willmore spheres
• An $\epsilon$-regularity result with mean curvature control for Willmore immersions and application to minimal bubbling
• A duality theorem for a four dimensional Willmore energy