MINIMAL SURFACES IN FINITE VOLUME NONCOMPACT HYPERBOLIC 3-MANIFOLDS

被引：16

作者：

Collin, Pascal ^{[1
]}

Hauswirth, Laurent ^{[2
]}

Mazet, Laurent ^{[3
]}

Rosenberg, Harold ^{[4
]}

机构：

[1] Univ Paul Sabatier, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse, France

[2] Univ Paris Est, CNRS, LAMA UMR 8050, UPEC,UPEM, F-77454 Marne La Vallee, France

[3] Univ Paris Est, CNRS, LAMA UMR 8050, UPEC,UPEM, 61 Ave Gen Gaulle, F-94010 Creteil, France

[4] Inst Nacl Matemat Pura & Aplicada IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, RJ, Brazil

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 369卷 / 06期

关键词：

EXISTENCE;

D O I：

10.1090/tran/6859

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove there exists a compact embedded minimal surface in a complete finite volume hyperbolic 3-manifold N. We also obtain a least area, incompressible, properly embedded, finite topology, 2-sided surface. We prove a properly embedded minimal surface of bounded curvature has finite topology. This determines its asymptotic behavior. Some rigidity theorems are obtained.

引用

页码：4293 / 4309

页数：17