Ricci curvature and Lp-convergence

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15 Citations (Scopus)

Abstract

We give the definition of Lp-convergence of tensor fields with respect to the Gromov-Hausdorff topology and several fundamental properties of the convergence. We apply this to establish a Bochner-type inequality which keeps the term of Hessian on the Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with a lower Ricci curvature bound and to give a geometric explicit formula for the Dirichlet Laplacian on a limit space defined by Cheeger-Colding. We also prove the continuity of the first eigenvalues of the p-Laplacian with respect to the Gromov-Hausdorff topology.

Original languageEnglish
Pages (from-to)85-154
Number of pages70
JournalJournal fur die Reine und Angewandte Mathematik
Volume2015
Issue number705
DOIs
Publication statusPublished - 2015 Aug 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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