Journal of the Institute of Mathematics of Jussieu

Research Article

Saddle towers and minimal k-noids in ℍ2 × ℝ

Filippo Morabitoa1 p1 and M. Magdalena Rodrígueza2

a1 Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Plaza de las Ciencias 3, 28040, Madrid, Spain

a2 Departamento de Geometría y Topología, Universidad de Granada, Fuentenueva s/n, 18071, Granada, Spain (


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.

(Received November 03 2009)

(Revised October 06 2010)

(Accepted October 06 2010)


  • saddle tower;
  • k-noid;
  • conjugation;
  • Jenkins–Serrin problem

AMS 2010 Mathematics subject classification

  • Primary 53A10; 49Q05; 58E12


p1 Present address: Korea Institute for Advanced Study, 207-43 Cheongnyangni 2-dong, Dongdaemungu, Seoul 130-722, Republic of Korea (