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Smoothing Riemannian metrics with Ricci curvature bounds

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Abstract

We prove that Riemannian metrics with an absolute Ricci curvature bound and a conjugate radius bound can be smoothed to having a sectional curvature bound. Using this we derive a number of results about structures of manifolds with Ricci curvature bounds.

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Author information

Author notes

  1. Guofang Wei

    Present address: Department of Mathematics, University of California, 93106, Santa Barbara, CA

Authors and Affiliations

  1. Department of Mathematics, University of Southern California, 90089, Los Angles, CA

    Xianzhe Dai

  2. Department of Mathematics, University of California, 93106, Santa Barbara, CA

    Rugang Ye

Authors
  1. Xianzhe Dai
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  2. Guofang Wei
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  3. Rugang Ye
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Additional information

The authors were supported in part by NSF Grant. The first author was also supported in part by Alfred P. Sloan Fellowship

This article was processed by the author using the LATEX style filecljourl from Springer-Verlag.

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Dai, X., Wei, G. & Ye, R. Smoothing Riemannian metrics with Ricci curvature bounds. Manuscripta Math 90, 49–61 (1996). https://doi.org/10.1007/BF02568293

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  • DOI: https://doi.org/10.1007/BF02568293

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