| Download ( PDF | 494kB) |
Volume comparison for hypersurfaces in Lorentzian manifolds and singularity theorems
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.Date of publication of this fulltext: 19 Mar 2012 07:35
Monograph
DOI to cite this document: 10.5283/epub.23578
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.
Involved Institutions
Details
| Item type | Monograph (Working Paper) | ||||||
| Series of the University of Regensburg: | Preprintreihe der Fakultät Mathematik | ||||||
|---|---|---|---|---|---|---|---|
| Volume: | 8/2012 | ||||||
| Date | 2012 | ||||||
| Institutions | Mathematics > Prof. Dr. Felix Finster | ||||||
| Classification |
| ||||||
| Keywords | Lorentzian geometry, comparison theorems, singularity theorems | ||||||
| Dewey Decimal Classification | 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 | ||||||
| URN of the UB Regensburg | urn:nbn:de:bvb:355-epub-235787 | ||||||
| Item ID | 23578 |
Export bibliographical data
Owner only: item control page
Download Statistics
Download Statistics