Tohoku Mathematical Journal
2000
September
SECOND SERIES VOL. 52, NO. 3

Tohoku Math. J.
52 (2000), 331-348

Title SOME SEMI-RIEMANNIAN VOLUME COMPARISON THEOREMS

Author Paul E. Ehrlich and Miguel Sánchez

(Received November 16, 1998)
Abstract. Lorentzian versions of classical Riemannian volume comparison theorems by Gunther, Bishop and Bishop-Gromov, are stated for suitable natural subsets of general semi-Riemannian manifolds. The problem is more subtle in the Bishop-Gromov case, which is extensively discussed. For the general semi-Riemannian case, a local version of the Gunther and Bishop theorems is given and applied.

2000 Mathematics Subject Classification. Primary 53C50; Secondary 53C21, 53C20.

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