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November 2015 Complete Willmore surfaces in $\mathbb{H}^3$ with bounded energy: Boundary regularity and bubbling
Spyros Alexakis, Rafe Mazzeo
J. Differential Geom. 101(3): 369-422 (November 2015). DOI: 10.4310/jdg/1445518919


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.


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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.


Published: November 2015
First available in Project Euclid: 22 October 2015

zbMATH: 1335.53076
MathSciNet: MR3415767
Digital Object Identifier: 10.4310/jdg/1445518919

Rights: Copyright © 2015 Lehigh University


Vol.101 • No. 3 • November 2015
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