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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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