Geometric analysis of Lorentzian distance function on spacelike hypersurfaces

Alías, Luis; Hurtado, Ana; Palmer, Vicente

doi:10.1090/S0002-9947-2010-04992-X

Geometric analysis of Lorentzian distance function on spacelike hypersurfaces
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by Luis J. Alías, Ana Hurtado and Vicente Palmer PDF

Trans. Amer. Math. Soc. 362 (2010), 5083-5106 Request permission

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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