Inventiones mathematicae

, Volume 133, Issue 1, pp 107–132

Uniqueness of the Riemann minimal examples

  • William H. Meeks III
  • Joaquín Pérez
  • Antonio Ros
Article

DOI: 10.1007/s002220050241

Cite this article as:
Meeks III, W., Pérez, J. & Ros, A. Invent math (1998) 133: 107. doi:10.1007/s002220050241

Abstract.

We prove that a properly embedded minimal surface in R 3 of genus zero with infinite symmetry group is a plane, a catenoid, a helicoid or a Riemann minimal example. We introduce the language of Hurwitz schemes to understand the underlying moduli space of surfaces in our setting.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • William H. Meeks III
    • 1
  • Joaquín Pérez
    • 2
  • Antonio Ros
    • 2
  1. 1.Mathematics Department, University of Massachusetts, Amherst, MA 01003, USAUS
  2. 2.Departamento de Geometría y Topología, Universidad de Granada, E-Fuentenueva, 18071 Granada, Spain (FAX: 34 58 243281)ES