Complete Willmore surfaces in H3 with bounded energy: boundary regularity and bubbling
arXiv:1204.4955
Abstract
We study various aspects related to boundary regularity of complete properly embedded Willmore surfaces in H3, 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 C1 boundary regularity. We examine the possible lack of C1 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.
Substantial revisions: basic energy hypothesis strengthened; the result now covers Willmore surfaces
References in corpus (5)
- Willmore Spheres in Compact Riemannian Manifolds
- Topics in conformally compact Einstein metrics
- Bubbling and regularity issues in geometric non-linear analysis
- Weak limit of an immersed surface sequence with bounded Willmore functional
- Multiple-layer solutions to the Allen-Cahn equation on hyperbolic space