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Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below

Gigli, Nicola ; Mondino, Andrea ; Rajala, Tapio

In: Journal für die reine und angewandte Mathematik (Crelles Journal), 2015, vol. 2015, no. 705, p. 233-244

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    Titel
    • Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below
    Autor
    • Gigli, Nicola. Mathématiques, Université de Nice, Parc Valrose, 06108 Nice, France
    • Mondino, Andrea. Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
    • Rajala, Tapio. Department of Mathematics and Statistics, P.O. Box, FI-40014 University of Jyväskylä, Finland
    Dokumententyp
    • Postprint
    Sprache
    • Englisch
    Veröffentlicht in
    • Journal für die reine und angewandte Mathematik (Crelles Journal), 2015, vol. 2015, no. 705, p. 233-244. De Gruyter
    Andere elektronische Ausgabe
    Klassifikation
    • Mathematik
    OAI-PMH-ID
    • oai:doc.rero.ch:325025
    Summary
    We show that in any infinitesimally Hilbertian 𝖢𝖣 * (K,N)$\mathsf {CD}^*(K,N)$ -space at almost every point there exists a Euclidean weak tangent, i.e., there exists a sequence of dilations of the space that converges to a Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof follows by considering iterated tangents and the splitting theorem for infinitesimally Hilbertian 𝖢𝖣 * (0,N)$\mathsf {CD}^*(0,N)$ -spaces.