Geometric & Functional Analysis GAFA

, Volume 7, Issue 6, pp 1031–1045

Relative Volume Comparison with Integral Curvature Bounds

  • P. Petersen
  • G. Wei

DOI: 10.1007/s000390050036

Cite this article as:
Petersen, P. & Wei, G. GAFA, Geom. funct. anal. (1997) 7: 1031. doi:10.1007/s000390050036


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.

Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • P. Petersen
    • 1
  • G. Wei
    • 2
  1. 1.Peter Petersen, Department of Mathematics, University of California, Los Angeles, CA 90095, USA, e-mail: petersen@math.ucla.eduUS
  2. 2.Guofang Wei, Department of Mathematics, University of California, Santa Barbara, CA 93106, USA, e-mail: wei@math.ucsb.eduUS

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