Metric measure geometry

2014/10/02 by Takashi Shioya, Shioya, Takashi · 1 citation
Mathematics · #53C23 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.MG #msc:53C23

paper · pdf · doi:10.48550/arxiv.1410.0428

172 pages; not a final version; to appear in the IRMA series of the European Mathematical Society

arxiv created 2014/10/02 · openalex publication_date 2014/10/02 · arxiv updated 2014/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this book, we study Gromov's metric geometric theory on the space of metric measure spaces, based on the idea of concentration of measure phenomenon due to Lévy and Milman. Although most of the details are omitted in the original article of Gromov, we present complete and detailed proofs for some main parts, in which we prove several claims that are not mentioned in any literature. We also discuss concentration with a lower bound of curvature, originally studied by Funano and the author.

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• Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry

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