Research output: Contribution to journal › Article

**Triply periodic constant mean curvature surfaces.** / H. Meeks III, William; Tinaglia, Giuseppe.

Research output: Contribution to journal › Article

H. Meeks III, W & Tinaglia, G 2018, 'Triply periodic constant mean curvature surfaces', *ADVANCES IN MATHEMATICS*, vol. 335, pp. 809-837. https://doi.org/10.1016/j.aim.2018.07.018

H. Meeks III, W., & Tinaglia, G. (2018). Triply periodic constant mean curvature surfaces. *ADVANCES IN MATHEMATICS*, *335*, 809-837. https://doi.org/10.1016/j.aim.2018.07.018

H. Meeks III W, Tinaglia G. Triply periodic constant mean curvature surfaces. ADVANCES IN MATHEMATICS. 2018 Sep 7;335:809-837. https://doi.org/10.1016/j.aim.2018.07.018

@article{8fb22ed851e54cf3b7bd6475cdd3745a,

title = "Triply periodic constant mean curvature surfaces",

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. ",

author = "{H. Meeks III}, William and Giuseppe Tinaglia",

year = "2018",

month = sep,

day = "7",

doi = "10.1016/j.aim.2018.07.018",

language = "English",

volume = "335",

pages = "809--837",

journal = "ADVANCES IN MATHEMATICS",

issn = "0001-8708",

publisher = "ACADEMIC PRESS INC",

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TY - JOUR

T1 - Triply periodic constant mean curvature surfaces

AU - H. Meeks III, William

AU - Tinaglia, Giuseppe

PY - 2018/9/7

Y1 - 2018/9/7

N2 - 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.

AB - 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.

U2 - 10.1016/j.aim.2018.07.018

DO - 10.1016/j.aim.2018.07.018

M3 - Article

VL - 335

SP - 809

EP - 837

JO - ADVANCES IN MATHEMATICS

JF - ADVANCES IN MATHEMATICS

SN - 0001-8708

ER -

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