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Comparison Geometry with Integral Curvature Bounds

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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.

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Authors and Affiliations

  1. Peter Petersen, Department of Mathematics, University of California, Los Angeles, CA 90095, USA, e-mail: petersen@math.ucla.edu, , , , , , US

    P. Peterson

  2. Semion D. Shteingold, Dept. of Mathematics, University of California, Los Angeles, CA 90095, USA, e-mail: shteingd@math.ucla.edu, , , , , , US

    S.D. Shteingold

  3. Guofang Wei, Department of Mathematics, University of California, Santa Barbara, CA 93106, USA, e-mail: wei@math.ucsb.edu, , , , , , US

    G. Wei

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  1. P. Peterson
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  2. S.D. Shteingold
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  3. G. Wei
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Submitted: August 1996, revised: July 1997

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Peterson, P., Shteingold, S. & Wei, G. Comparison Geometry with Integral Curvature Bounds. GAFA, Geom. funct. anal. 7, 1011–1030 (1997). https://doi.org/10.1007/s000390050035

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  • DOI: https://doi.org/10.1007/s000390050035

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