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Saddle towers and minimal k-noids in ℍ2 × ℝ

Part of: Classical differential geometry

Published online by Cambridge University Press:  21 June 2011

Filippo Morabito  and
M. Magdalena Rodríguez
Filippo Morabito
Affiliation:
Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Plaza de las Ciencias 3, 28040, Madrid, Spain
M. Magdalena Rodríguez
Affiliation:
Departamento de Geometría y Topología, Universidad de Granada, Fuentenueva s/n, 18071, Granada, Spain ([email protected])
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Abstract

Given k ≥ 2, we construct a (2k − 2)-parameter family of properly embedded minimal surfaces in ℍ2 × ℝ invariant by a vertical translation T, called saddle towers, which have total intrinsic curvature 4π(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 4π(1 − k), genus zero and k vertical planar ends.

Keywords

saddle towerk-noidconjugationJenkins–Serrin problem

MSC classification

Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 2 , April 2012 , pp. 333 - 349
Copyright
Copyright © Cambridge University Press 2012

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