An $\epsilon$-regularity result with mean curvature control for Willmore immersions and application to minimal bubbling

Abstract

In this paper we prove a convergence result for sequences of Willmore immersions with simple minimal bubbles. To this end we replace the total curvature control in T. Rivière's proof of the $\epsilon$-regularity for Willmore immersions by a control of the local Willmore energy.

42 pages, 2 figures, new version after reviewer's comments for publication

References in corpus (3)

• Energy Quantization of Willmore surfaces at the boundary of the Moduli Space
• Minimal Bubbling for Willmore Surfaces
• Asymptotic analysis for surfaces with large constant mean curvature and free boundaries

Cited by in corpus (1)

• Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications