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Classification of doubly-periodic minimal surfaces of genus zero

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Inventiones mathematicae Aims and scope

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.

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Authors and Affiliations

  1. Centre de Mathématiques, Ecole Polytechnique, URA 169 du CNRS, 91128 Palaiseau, France (e-mail: lazard@cmat.polytechnique.fr), , , , , , FR

    Hippolyte Lazard-Holly

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

    William H. Meeks III

Authors
  1. Hippolyte Lazard-Holly
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  2. William H. Meeks III
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Oblatum 30-IX-1998 & 18-II-2000¶Published online: 30 October 2000

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Lazard-Holly, H., Meeks III, W. Classification of doubly-periodic minimal surfaces of genus zero. Invent. math. 143, 1–27 (2001). https://doi.org/10.1007/PL00005796

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  • DOI: https://doi.org/10.1007/PL00005796

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