Triply periodic constant mean curvature surfaces

被引：7

作者：

Meeks, William H., III ^{[1
]}

Tinaglia, Giuseppe ^{[2
]}

机构：

[1] Univ Massachusetts, Math Dept, Amherst, MA 01003 USA

[2] Kings Coll London, Dept Math, London WC2R 2LS, England

来源：

ADVANCES IN MATHEMATICS | 2018年 / 335卷

基金：

英国工程与自然科学研究理事会;

关键词：

Minimal surface; Constant mean curvature; H-lamination; Injectivity radius; Curvature estimates; Area estimates; MINIMAL-SURFACES; EMBEDDED SURFACES; H-SURFACES; UNIQUENESS; EXISTENCE; GENUS;

D O I：

10.1016/j.aim.2018.07.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a closed flat 3-torus N, for each H > 0 and each non-negative 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 not equal 2, connected closed embedded minimal surfaces of genus g with arbitrarily large area. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：809 / 837

页数：29

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