Inventiones mathematicae

, Volume 143, Issue 1, pp 1–27

Classification of doubly-periodic minimal surfaces of genus zero

  • Hippolyte Lazard-Holly
  • William H. Meeks III

DOI: 10.1007/PL00005796

Cite this article as:
Lazard-Holly, H. & Meeks III, W. Invent. math. (2001) 143: 1. doi:10.1007/PL00005796


We prove that if the quotient surface of a properly embedded doubly–periodic minimal surface in ℝ3 has genus zero, then the surface is one of the classical Scherk examples.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Hippolyte Lazard-Holly
    • 1
  • William H. Meeks III
    • 2
  1. 1.Centre de Mathématiques, Ecole Polytechnique, URA 169 du CNRS, 91128 Palaiseau, France (e-mail:
  2. 2.Department of Mathematics, Lederle Graduate Research Center, University of Massachusetts, Amherst, MA 01003-4515, USA (e-mail: