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Inventiones mathematicae

, Volume 143, Issue 1, pp 1–27 | Cite as

Classification of doubly-periodic minimal surfaces of genus zero

  • Hippolyte Lazard-Holly
  • William H. Meeks III

Abstract.

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.

Keywords

Minimal Surface Genus Zero Periodic Minimal Surface Quotient Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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: lazard@cmat.polytechnique.fr)FR
  2. 2.Department of Mathematics, Lederle Graduate Research Center, University of Massachusetts, Amherst, MA 01003-4515, USA (e-mail: bill@gang.umass.edu)US

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