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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Geometric analysis of Lorentzian distance function on spacelike hypersurfaces


Authors: Luis J. Alías, Ana Hurtado and Vicente Palmer
Journal: Trans. Amer. Math. Soc. 362 (2010), 5083-5106
MSC (2010): Primary 53C50, 53C42, 31C05
Published electronically: May 25, 2010
MathSciNet review: 2657673
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Abstract: Some analysis on the Lorentzian distance in a spacetime with controlled sectional (or Ricci) curvatures is done. In particular, we focus on the study of the restriction of such distance to a spacelike hypersurface satisfying the Omori-Yau maximum principle. As a consequence, and under appropriate hypotheses on the (sectional or Ricci) curvatures of the ambient spacetime, we obtain sharp estimates for the mean curvature of those hypersurfaces. Moreover, we also give a sufficient condition for its hyperbolicity.


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Additional Information

Luis J. Alías
Affiliation: Departamento de Matemáticas, Universidad de Murcia, E-30100 Espinardo, Murcia, Spain
Email: ljalias@um.es

Ana Hurtado
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain
Email: ahurtado@ugr.es

Vicente Palmer
Affiliation: Departament de Matemàtiques, Universitat Jaume I, E-12071 Castelló, Spain
Email: palmer@mat.uji.es

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-04992-X
PII: S 0002-9947(2010)04992-X
Keywords: Lorentzian distance function, Lorentzian index form, spacelike hypersurface, transience, Brownian motion, mean curvature, function theory on manifolds.
Received by editor(s): March 7, 2008
Published electronically: May 25, 2010
Additional Notes: This research is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Regional Agency for Science and Technology (Regional Plan for Science and Technology 2007-2010).
The research of the first author was partially supported by MEC project MTM2007-64504 and Fundación Séneca project 04540/GERM/06, Spain
The second author was supported by Spanish MEC-DGI grant No. MTM2007-62344, the Bancaixa-Caixa Castelló Foundation and Junta de Andalucía grants PO6-FQM-5088 and FQM325.
The third author was supported by Spanish MEC-DGI grant No. MTM2007-62344 and the Bancaixa-Caixa Castelló Foundation
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.