COUNTING MINIMAL SURFACES IN QUASI-FUCHSIAN THREE-MANIFOLDS

被引：17

作者：

Huang, Zheng ^{[1
,2
]}

Wang, Biao ^{[3
]}

机构：

[1] CUNY, Dept Math, Staten Isl, NY 10314 USA

[2] CUNY, Grad Ctr, New York, NY 10016 USA

[3] Wesleyan Univ, Dept Math, Middletown, CT 06459 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 367卷 / 09期

基金：

美国国家科学基金会;

关键词：

HYPERSURFACES; EXISTENCE; MANIFOLDS; TOPOLOGY;

D O I：

10.1090/tran/6172

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well known that every quasi-Fuchsian manifold admits at least one closed incompressible minimal surface, and at most finitely many stable ones. In this paper, for any prescribed integer N > 0, we construct a quasi-Fuchsian manifold which contains at least 2(N) such minimal surfaces. As a consequence, there exists some simple closed Jordan curve on S-infinity(2) such that there are at least 2(N) disk-type complete minimal surfaces in H-3 sharing this Jordan curve as the asymptotic boundary.

引用

页码：6063 / 6083

页数：21

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