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
收藏
页码：4293 / 4309
页数：17
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