Elliptic PDEs on compact ricci limit spaces and applications

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7 Citations (Scopus)


In this paper we study elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular we establish continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. We apply these to the study of second-order differential calculus on such limit spaces.

Original languageEnglish
Pages (from-to)1-104
Number of pages104
JournalMemoirs of the American Mathematical Society
Issue number1211
Publication statusPublished - 2018 May


  • Elliptic PDEs
  • Gromov-Hausdorff convergence
  • Ricci curvature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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