Triply periodic constant mean curvature surfaces

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

SN - 0001-8708

VL - 335

SP - 809

EP - 837

JO - ADVANCES IN MATHEMATICS

JF - ADVANCES IN MATHEMATICS

ER -