Geometric & Functional Analysis GAFA

, Volume 7, Issue 6, pp 1011–1030

Comparison Geometry with Integral Curvature Bounds

  • P. Peterson
  • S.D. Shteingold
  • G. Wei

DOI: 10.1007/s000390050035

Cite this article as:
Peterson, P., Shteingold, S. & Wei, G. GAFA, Geom. funct. anal. (1997) 7: 1011. doi:10.1007/s000390050035

Abstract.

In this paper we shall generalize a formula of Heintze and Karcher for the volume of normal tubes around geodesics to a situation where one has integral bounds for the sectional curvature. This formula leads to a generalization of Cheeger's lemma for the length of the shortest closed geodesic and to a generalization of the Grove-Petersen finiteness result to a situation where one has integral curvature bounds.

Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • P. Peterson
    • 1
  • S.D. Shteingold
    • 2
  • G. Wei
    • 3
  1. 1.Peter Petersen, Department of Mathematics, University of California, Los Angeles, CA 90095, USA, e-mail: petersen@math.ucla.eduUS
  2. 2.Semion D. Shteingold, Dept. of Mathematics, University of California, Los Angeles, CA 90095, USA, e-mail: shteingd@math.ucla.eduUS
  3. 3.Guofang Wei, Department of Mathematics, University of California, Santa Barbara, CA 93106, USA, e-mail: wei@math.ucsb.eduUS