Deutsch
Treude, Jan-Hendrik and Grant, James D.E. (2012) Volume comparison for hypersurfaces
in Lorentzian manifolds and singularity
theorems. Preprintreihe der Fakultät Mathematik 8/2012, Working Paper.
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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: | Monograph (Working Paper) | ||||||
|---|---|---|---|---|---|---|---|
| Institutions: | Mathematics > Prof. Dr. Felix Finster | ||||||
| Classification: |
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| Keywords: | Lorentzian geometry, comparison theorems, singularity theorems | ||||||
| Subjects: | 500 Science > 510 Mathematics | ||||||
| Status: | Unknown | ||||||
| Refereed: | No, this version has not been refereed yet (as with preprints) | ||||||
| Created at the University of Regensburg: | Yes | ||||||
| Owner: | Universitätsbibliothek Regensburg | ||||||
| Deposited On: | 19 Mar 2012 08:35 | ||||||
| Last Modified: | 19 Mar 2012 08:35 | ||||||
| Item ID: | 23578 |
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