The Willmore functional on complete minimal surfaces in H3: boundary regularity and bubbling

Details The Willmore functional on complete minimal surfaces in H3: boundary regularity and bubbling The Willmore functional on complete minimal surfaces in H3: boundary regularity and bubbling

2012-04-23

arxiv.org/abs/1204.4955v1

Mathematics

Differential Geometry

36 pages

Scientific paper

We study various aspects related to boundary regularity of complete properly embedded minimal surfaces in H3, particularly those related to assumptions on boundedness or smallness of Willmore energy. We prove, in particular, that small energy gives control on C1 boundary regularity. We examine the possible lack of convergence in the C1 norm for sequences of finite energy minimal surfaces; we find that the mechanism responsible for this is a bubbling phenomenon of energy escaping to infinity.

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