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

共 50 条

[21] On the complexity and volume of hyperbolic 3-manifolds
Thomas Delzant
Leonid Potyagailo
Israel Journal of Mathematics, 2013, 193 : 209 - 232
[22] On the renormalized volume of hyperbolic 3-manifolds
Krasnov, Kirill
Schlenker, Jean-Marc
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 279 (03) : 637 - 668
[23] On the complexity and volume of hyperbolic 3-manifolds
Delzant, Thomas
Potyagailo, Leonid
ISRAEL JOURNAL OF MATHEMATICS, 2013, 193 (01) : 209 - 232
[24] On the Renormalized Volume of Hyperbolic 3-Manifolds
Kirill Krasnov
Jean-Marc Schlenker
Communications in Mathematical Physics, 2008, 279 : 637 - 668
[25] EXTENDING FINITE-GROUP ACTIONS ON SURFACES TO HYPERBOLIC 3-MANIFOLDS
GRADOLATO, M
ZIMMERMANN, B
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1995, 117 : 137 - 151
[26] ON PROPERLY EMBEDDING NONCOMPACT SURFACES IN ARBITRARY 3-MANIFOLDS
BRIN, MG
THICKSTUN, TL
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1987, 54 : 350 - 366
[27] Minimal surfaces and particles in 3-manifolds
Krasnov, Kirill
Schlenker, Jean-Marc
GEOMETRIAE DEDICATA, 2007, 126 (01) : 187 - 254
[28] Minimal surfaces and particles in 3-manifolds
Kirill Krasnov
Jean-Marc Schlenker
Geometriae Dedicata, 2007, 126 : 187 - 254
[29] Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups
Liu, Yi
INVENTIONES MATHEMATICAE, 2023, 231 (02) : 741 - 804
[30] Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups
Yi Liu
Inventiones mathematicae, 2023, 231 : 741 - 804

← 1 2 3 4 5 →