Estimates for the volume of a Lorentzian manifold

被引:2
作者
Gerhardt, C [1 ]
机构
[1] Univ Heidelberg, Inst Angew Math, D-69120 Heidelberg, Germany
关键词
Lorentzian manifold; volume estimates; cosmological spacetime; general relativity; constant mean curvature; CMC hypersurface;
D O I
10.1023/A:1022336925552
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We prove new estimates for the volume of a Lorentzian manifold and show especially that cosmological spacetimes with crushing singularities have finite volume.
引用
收藏
页码:201 / 207
页数:7
相关论文
共 50 条
[41]   Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements [J].
Capdeboscq, Y ;
Vogelius, MS .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2003, 37 (02) :227-240
[42]   Holonomy groups of Lorentzian manifolds [J].
Galaev, A. S. .
RUSSIAN MATHEMATICAL SURVEYS, 2015, 70 (02) :249-298
[43]   Hyperbolic PDE and Lorentzian geometry [J].
Christodoulou, Demetrios .
PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL I, 2014, :259-282
[44]   On Lorentzian Connections with Parallel Skew Torsion [J].
Ernst, Igor ;
Galaev, Anton S. .
DOCUMENTA MATHEMATICA, 2022, 27 :2333-2383
[45]   Stable maximal hypersurfaces in Lorentzian spacetimes [J].
Colombo, Giulio ;
Pelegrin, Jose A. S. ;
Rigoli, Marco .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 179 :354-382
[46]   The twistor equation in Lorentzian spin geometry [J].
Helga Baum ;
Felipe Leitner .
Mathematische Zeitschrift, 2004, 247 :795-812
[47]   Lorentzian surfaces and the curvature of the Schmidt metric [J].
Sanchez, Y. Sanchez ;
Merlin, C. ;
Reynoso Fuentes, R. .
REVISTA MEXICANA DE FISICA, 2018, 64 (04) :429-438
[48]   Periodic trajectories on stationary Lorentzian manifolds [J].
Bartolo, R .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 43 (07) :883-903
[49]   Some concave functions on Lorentzian manifolds [J].
Reza Mirzaie ;
Omid Rezaei .
Mathematical Sciences, 2022, 16 :317-322
[50]   Lorentzian Legendrian mean curvature flow [J].
Lars Schäfer .
Mathematische Zeitschrift, 2013, 274 :1093-1111