Treude, Jan-Hendrik and Grant, James D. E. (2013) Volume comparison for hypersurfaces in Lorentzian manifolds and singularity theorems. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 43 (3). pp. 233-251. ISSN 0232-704X,
Full text not available from this repository. (Request a copy)Abstract
We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on the mean curvature of the hypersurface. Using these results, we give a new proof of Hawking's singularity theorem.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | METRIC-MEASURE-SPACES; CURVATURE; GEOMETRY; Lorentzian manifolds; Comparison geometry; Singularity theorems |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 24 Apr 2020 04:39 |
| Last Modified: | 24 Apr 2020 04:39 |
| URI: | https://pred.uni-regensburg.de/id/eprint/17082 |
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