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jenkins–serrin problem

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

Saddle towers and minimal k-noids in ℍ2 × ℝ
Part of
- Classical differential geometry
Filippo Morabito, M. Magdalena Rodríguez
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 11 / Issue 2 / April 2012

Published online by Cambridge University Press:

21 June 2011, pp. 333-349

Print publication:

April 2012
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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.