SADDLE TOWERS AND MINIMAL k-NOIDS IN H-2 x R

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Given k >= 2, we construct a (2k - 2)-parameter family of properly embedded minimal surfaces in H-2 x R invariant by a vertical translation T, called saddle towers, which have total intrinsic curvature 4 pi(1 - k), genus zero and 2k vertical Scherk-type ends in the quotient by T. Each of those examples is obtained from the conjugate graph of a Jenkins-Serrin graph over a convex polygonal domain with 2k edges of the same (finite) length. As limits of saddle towers, we obtain properly embedded minimal surfaces, called minimal k-noids, which are symmetric with respect to a horizontal slice (in fact they are vertical bi-graphs) and have total intrinsic curvature 4 pi(1 - k), genus zero and k vertical planar ends.
Publisher
CAMBRIDGE UNIV PRESS
Issue Date
2012-04
Language
English
Article Type
Article
Citation

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, v.11, no.2, pp.333 - 349

ISSN
1474-7480
DOI
10.1017/S1474748011000107
URI
http://hdl.handle.net/10203/191185
Appears in Collection
MA-Journal Papers(저널논문)
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