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Anderson-Cheeger limits of smooth Riemannian manifolds, and other Gromov-Hausdorff limits

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Abstract

We establish further regularity of the Cα and H1,p limits of smooth, n-dimensional Riemannian manifolds with a lower bound on Ricci tensor and injectivity radius, and an upper bound on volume, first considered in [1]. We use this extra regularity to show that such a limit is a nonbranching geodesic space, as defined in [10], and to construct a variant of a geodesic flow for such a limit. We contrast the behavior of some slightly more singular limits.

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Authors and Affiliations

  1. Mathematics Department, University of North Carolina, 27599, Chapel Hill, NC

    Michael Taylor

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  1. Michael Taylor
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Communicated by Claude LeBrun

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Taylor, M. Anderson-Cheeger limits of smooth Riemannian manifolds, and other Gromov-Hausdorff limits. J Geom Anal 17, 365–374 (2007). https://doi.org/10.1007/BF02930728

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  • DOI: https://doi.org/10.1007/BF02930728

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