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On scalar curvature rigidity of vacuum static spaces
- Source :
- Mathematische Annalen, vol 365, iss 3-4, Qing, J; & Yuan, W. (2016). On scalar curvature rigidity of vacuum static spaces. MATHEMATISCHE ANNALEN, 365(3-4), 1257-1277. doi: 10.1007/s00208-015-1302-0. UC Santa Cruz: Retrieved from: http://www.escholarship.org/uc/item/55c6k9ht, MATHEMATISCHE ANNALEN, vol 365, iss 3-4
- Publication Year :
- 2016
- Publisher :
- eScholarship, University of California, 2016.
-
Abstract
- In this paper we extend the local scalar curvature rigidity result in [6] to a small domain on general vacuum static spaces, which confirms the interesting dichotomy of local surjectivity and local rigidity about the scalar curvature in general in the light of the paper [10]. We obtain the local scalar curvature rigidity of bounded domains in hyperbolic spaces. We also obtain the global scalar curvature rigidity for conformal deformations of metrics in the domains, where the lapse functions are positive, on vacuum static spaces with positive scalar curvature, and show such domains are maximal, which generalizes the work in [15].<br />Comment: 14 pages, new references added, a few typo fixed
- Subjects :
- Mathematics - Differential Geometry
010308 nuclear & particles physics
Prescribed scalar curvature problem
Applied Mathematics
General Mathematics
010102 general mathematics
Mathematical analysis
Work (physics)
Conformal map
Curvature
01 natural sciences
Pure Mathematics
Domain (mathematical analysis)
General Relativity and Quantum Cosmology
Rigidity (electromagnetism)
math.DG
Differential Geometry (math.DG)
Bounded function
0103 physical sciences
FOS: Mathematics
Mathematics::Differential Geometry
0101 mathematics
Scalar curvature
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Mathematische Annalen, vol 365, iss 3-4, Qing, J; & Yuan, W. (2016). On scalar curvature rigidity of vacuum static spaces. MATHEMATISCHE ANNALEN, 365(3-4), 1257-1277. doi: 10.1007/s00208-015-1302-0. UC Santa Cruz: Retrieved from: http://www.escholarship.org/uc/item/55c6k9ht, MATHEMATISCHE ANNALEN, vol 365, iss 3-4
- Accession number :
- edsair.doi.dedup.....3e277d3bf4fd2a7feca6228824f6eed0