Compactness properties of the space of genus-g helicoids

Details Compactness properties of the space of genus-g helicoids Compactness properties of the space of genus-g helicoids

2009-07-03

arxiv.org/abs/0907.0522v1

Mathematics

Differential Geometry

11 pages

Scientific paper

In \cite{CM5}, Colding and Minicozzi describe a type of compactness property possessed by sequences of embedded minimal surfaces in $\Real^3$ with finite genus and with boundaries going to $\infty$. They show that any such sequence either contains a sub-sequence with uniformly bounded curvature or the sub-sequence has certain prescribed singular behavior. In this paper, we sharpen their description of the singular behavior when the surfaces have connected boundary. Using this, we deduce certain additional compactness properties of the space of genus-$g$ helicoids.

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