On the global evolution problem in 2+1 gravity

被引：37

作者：

Andersson, L ^{[1
]}

Moncrief, V

Tromba, AJ

机构：

[1] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

[2] Yale Univ, Dept Math, New Haven, CT 06520 USA

[3] Yale Univ, Dept Phys, New Haven, CT 06520 USA

[4] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 1997年 / 23卷 / 3-4期

关键词：

Lorentzian manifolds; foliations;

D O I：

10.1016/S0393-0440(97)87804-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Existence of global constant mean curvature (CMC) foliations of constant curvature 3-dimensional maximal globally hyperbolic Lorentzian manifolds, containing a constant mean curvature hypersurface with genus(Sigma) > 1, is proved. Constant curvature 3-dimensional Lorentzian manifolds can be viewed as solutions to the 2 + 1 vacuum Einstein equations with a cosmological constant. The proof is based on the reduction of the corresponding Hamiltonian system in CMC gauge to a time-dependent Hamiltonian system on the cotangent bundle of Teichmuller space. Estimates of the Dirichlet energy of the induced metric play an essential role in the proof.

引用

页码：191 / 205

页数：15