Volume comparison between spacelike hypersurfaces in a Lorentzian manifold with integral Ricci curvature bounds

被引：2

作者：

Paeng, Seong-Hun ^{[1
]}

机构：

[1] Konkuk Univ, Dept Math, Seoul 143701, South Korea

来源：

GENERAL RELATIVITY AND GRAVITATION | 2011年 / 43卷 / 08期

关键词：

Lorentzian manifold; Spacelike hypersurface; Integral Ricci curvature bound; Generalized Ricci tensor; (weighted) Volume comparison; METRIC-MEASURE-SPACES; COMPARISON-THEOREMS; EXPANSION RATE; GEOMETRY; EQUATIONS; TENSOR;

D O I：

10.1007/s10714-010-1106-1

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

We obtain the volume comparison between spacelike hypersurfaces in a Lorentzian manifold with integral Ricci and mean curvature bounds. Also we extend volume comparisons to weighted volume comparisons with integral norms of the generalized Ricci tensor.

引用

页码：2089 / 2102

页数：14

共 19 条

[1] [Anonymous], LECT NOTES MATH
[2] Volume comparison theorems for Lorentzian manifolds
Ehrlich, PE
Jung, YT
Kim, SB
[J]. GEOMETRIAE DEDICATA, 1998, 73 (01) : 39 - 56
[3] Some semi-Riemannian volume comparison theorems
Ehrlich, PE
Sánchez, M
[J]. TOHOKU MATHEMATICAL JOURNAL, 2000, 52 (03) : 331 - 348
[4] The upperbound of the volume expansion rate in a Lorentzian manifold
Kim, Jong Ryul
[J]. GENERAL RELATIVITY AND GRAVITATION, 2010, 42 (02) : 403 - 412
[5] Some geometric properties of the Bakry-Emery-Ricci tensor
Lott, J
[J]. COMMENTARII MATHEMATICI HELVETICI, 2003, 78 (04) : 865 - 883
[6] Ricci curvature for metric-measure spaces via optimal transport
Lott, John
Villani, Cedric
[J]. ANNALS OF MATHEMATICS, 2009, 169 (03) : 903 - 991
[7] ONEIL B, 2001, SEMIRIEMANNIAN GEOME
[8] The geometry of dissipative evolution equations: The porous medium equation
Otto, F
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (1-2) : 101 - 174
[9] Volume expansion rate of the Lorentzian manifold based on integral Ricci curvature over a timelike geodesic
Paeng, Seong-Hun
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2007, 57 (06) : 1499 - 1503
[10] Distance to a focal point and singularity theorems with weak timelike convergence condition
Paeng, Seong-Hun
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2009, 146 : 475 - 487

← 1 2 →