Complete Willmore surfaces in H3 with bounded energy: boundary\n regularity and bubbling

2012/04/22 by Spyros Alexakis, Rafe Mazzeo, Alexakis, Spyros +1 · 1 citation
Computer Science · Mathematics · #35J70 #53A10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1204.4955

openalex publication_date 2012/04/22 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

We study various aspects related to boundary regularity of complete properly\nembedded Willmore surfaces in H3, particularly those related to assumptions on\nboundedness or smallness of a certain weighted version of the Willmore energy.\nWe prove, in particular, that small energy controls C1 boundary regularity. We\nexamine the possible lack of C1 convergence for sequences of surfaces with\nbounded Willmore energy and find that the mechanism responsible for this is a\nbubbling phenomenon, where energy escapes to infinity.\n

Citations

• Topics in conformally compact Einstein metrics
• Weak limit of an immersed surface sequence with bounded Willmore functional
• Existence an regularity of constant mean curvature hypersurfaces in hyperbolic space
• Multiple-layer solutions to the Allen-Cahn equation on hyperbolic space

Cited by

• Asymptotic behavior of geodesics in conformally compact manifolds

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