A weakly second-order differential structure on rectifiable metric measure spaces

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11 Citations (Scopus)

Abstract

We give a definition of angles on the Gromov-Hausdorff limit space of a sequence of complete n-dimensional Riemannian manifolds with a lower Ricci curvature bound. We apply this to prove there is a weakly second-order differential structure on these spaces and prove that they admit a unique Levi-Civita connection, allowing us to define the Hessian of a twice differentiable function.

Original languageEnglish
Pages (from-to)633-668
Number of pages36
JournalGeometry and Topology
Volume18
Issue number2
DOIs
Publication statusPublished - 2014
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology

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