## Regularity of Lorentzian Busemann Functions

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- by Gregory J. Galloway and Arnaldo Horta PDF
- Trans. Amer. Math. Soc.
**348**(1996), 2063-2084 Request permission

## Abstract:

A general theory of regularity for Lorentzian Busemann functions in future timelike geodesically complete spacetimes is presented. This treatment simplifies and extends the local regularity developed by Eschenburg, Galloway and Newman to prove the Lorentzian splitting theorem. Criteria for global regularity are obtained and used to improve results in the literature pertaining to a conjecture of Bartnik.## References

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## Additional Information

**Gregory J. Galloway**- Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33124
- MR Author ID: 189210
- Email: galloway@math.miami.edu
**Arnaldo Horta**- Affiliation: National Security Agency, Fort Meade, Maryland 20755-6000
- Email: ahorta@ix.netcom.com
- Received by editor(s): September 9, 1994
- Additional Notes: The first author was partially supported by NSF grant DMS-9204372.
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**348**(1996), 2063-2084 - MSC (1991): Primary 53C50
- DOI: https://doi.org/10.1090/S0002-9947-96-01587-5
- MathSciNet review: 1348150