Gluing constructions for asymptotically hyperbolic manifolds with constant scalar curvature

被引：0

作者：

Chrusciel, Piotr T. ^{[1
,2
,3
]}

Delay, Erwann ^{[4
]}

机构：

[1] LMPT, Tours, France

[2] Math Inst, Oxford OX1 3LB, England

[3] Univ Oxford Hertford Coll, Oxford OX1 3BW, England

[4] Fac Sci, Lab Anal Non Lineaire & Geometrie, F-84000 Avignon, France

来源：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2009年 / 17卷 / 02期

关键词：

EINSTEIN CONSTRAINT EQUATIONS; RIEMANNIAN-MANIFOLDS; MASS; EXISTENCE; VACUUM;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that asymptotically hyperbolic initial data satisfying smallness conditions in dimensions n >= 3, or fast decay conditions in n >= 5, or a genericity condition in n >= 9, can be deformed, by a deformation that is supported arbitrarily far in the asymptotic region, to ones that are exactly Kottler ("Schwarzschild-adS") in the asymptotic region.

引用

页码：343 / 381

页数：39

共 50 条

[1] Gluing theorems for constant scalar curvature manifolds
Byde, A
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2003, 52 (05) : 1147 - 1199
[2] PERTURBATIVE SOLUTIONS TO THE EXTENDED CONSTANT SCALAR CURVATURE EQUATIONS ON ASYMPTOTICALLY HYPERBOLIC MANIFOLDS
Delay, Erwann
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (07) : 2293 - 2298
[3] SCALAR CURVATURE RIGIDITY OF ASYMPTOTICALLY HYPERBOLIC SPIN MANIFOLDS
MINOO, M
MATHEMATISCHE ANNALEN, 1989, 285 (04) : 527 - 539
[4] Scalar Curvature Rigidity for Asymptotically Locally Hyperbolic Manifolds
Lars Andersson
Mattias Dahl
Annals of Global Analysis and Geometry, 1998, 16 : 1 - 27
[5] Scalar curvature rigidity for asymptotically locally hyperbolic manifolds
Andersson, L
Dahl, M
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 1998, 16 (01) : 1 - 27
[6] Constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds
Sakovich, Anna
CLASSICAL AND QUANTUM GRAVITY, 2010, 27 (24)
[7] Exhaustion of isoperimetric regions in asymptotically hyperbolic manifolds with scalar curvature R ≥-6
Ji, Dandan
Shi, Yuguang
Zhu, Bo
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2018, 26 (03) : 627 - 658
[8] Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation
Gicquaud, Romain
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2023, 31 (08)
[9] Curvature estimates in asymptotically flat manifolds of positive scalar curvature
Finster, F
Kath, I
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2002, 10 (05) : 1017 - 1031
[10] Existence and Uniqueness of Constant Mean Curvature Foliation of Asymptotically Hyperbolic 3-Manifolds
Neves, Andre
Tian, Gang
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2009, 19 (03) : 910 - 942

← 1 2 3 4 5 →