, Volume 7, Issue 6, pp 1031-1045

Relative Volume Comparison with Integral Curvature Bounds

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Abstract.

In this paper we shall generalize the Bishop-Gromov relative volume comparison estimate to a situation where one only has an integral bound for the part of the Ricci curvature which lies below a given number. This will yield several compactness and pinching theorems.

Submitted: August 1996, revised: July 1997