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Regularity of Lorentzian Busemann Functions


Authors: Gregory J. Galloway and Arnaldo Horta
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
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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.


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Additional Information

Gregory J. Galloway
Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33124
Email: galloway@math.miami.edu

Arnaldo Horta
Affiliation: National Security Agency, Fort Meade, Maryland 20755-6000
Email: ahorta@ix.netcom.com

DOI: https://doi.org/10.1090/S0002-9947-96-01587-5
Received by editor(s): September 9, 1994
Additional Notes: The first author was partially supported by NSF grant DMS-9204372.
Article copyright: © Copyright 1996 American Mathematical Society

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