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Triply periodic constant mean curvature surfaces

Research output: Contribution to journalArticle

William H. Meeks III, Giuseppe Tinaglia

Original languageEnglish
Pages (from-to)809-837
JournalADVANCES IN MATHEMATICS
Early online date26 Jul 2018
DOIs
Accepted/In press2 Jul 2018
E-pub ahead of print26 Jul 2018
Published7 Sep 2018

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Abstract

Given a closed flat 3-torus N, for each H > 0 and each nonnegative integer g, we obtain area estimates for closed surfaces with genus g and constant mean curvature H embedded in N. This result contrasts with the theorem of Traizet [31], who proved that every flat 3-torus admits for every positive integer g with g = 2, connected closed embedded minimal surfaces of genus g with arbitrarily large area.

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