Abstract
We study various aspects related to boundary regularity of complete properly embedded Willmore surfaces in $\mathbb{H}^3$, particularly those related to assumptions on boundedness or smallness of a certain weighted version of the Willmore energy. We prove, in particular, that small energy controls $\mathcal{C}^1$ boundary regularity. We examine the possible lack of $\mathcal{C}^1$ convergence for sequences of surfaces with bounded Willmore energy and find that the mechanism responsible for this is a bubbling phenomenon, where energy escapes to infinity.
Citation
Spyros Alexakis. Rafe Mazzeo. "Complete Willmore surfaces in $\mathbb{H}^3$ with bounded energy: Boundary regularity and bubbling." J. Differential Geom. 101 (3) 369 - 422, November 2015. https://doi.org/10.4310/jdg/1445518919
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