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Metric Measure Geometry: Gromov’s Theory of Convergence and Concentration of Metrics and Measures
 
Takashi Shioya Tohoku University, Mathematical Institute, Sendai, Japan
A publication of European Mathematical Society
Metric Measure Geometry
Hardcover ISBN:  978-3-03719-158-3
Product Code:  EMSILMTP/25
List Price: $48.00
AMS Member Price: $38.40
Please note AMS points can not be used for this product
Metric Measure Geometry
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Metric Measure Geometry: Gromov’s Theory of Convergence and Concentration of Metrics and Measures
Takashi Shioya Tohoku University, Mathematical Institute, Sendai, Japan
A publication of European Mathematical Society
Hardcover ISBN:  978-3-03719-158-3
Product Code:  EMSILMTP/25
List Price: $48.00
AMS Member Price: $38.40
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS IRMA Lectures in Mathematics and Theoretical Physics
    Volume: 252016; 194 pp
    MSC: Primary 53; Secondary 28; 30; 35; 54; 58; 60

    This book studies a new theory of metric geometry on metric measure spaces. The theory was originally developed by M. Gromov in his book Metric Structures for Riemannian and Non-Riemannian Spaces and based on the idea of the concentration of measure phenomenon by Lévy and Milman. A central theme in this book is the study of the observable distance between metric measure spaces, defined by the difference between 1-Lipschitz functions on one space and those on the other. The topology on the set of metric measure spaces induced by the observable distance function is weaker than the measured Gromov–Hausdorff topology and allows the author to investigate a sequence of Riemannian manifolds with unbounded dimensions.

    One of the main parts of this presentation is the discussion of a natural compactification of the completion of the space of metric measure spaces. The stability of the curvature-dimension condition is also discussed.

    A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.

    Readership

    Graduate students and research mathematicians interested in metric measure spaces.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 252016; 194 pp
MSC: Primary 53; Secondary 28; 30; 35; 54; 58; 60

This book studies a new theory of metric geometry on metric measure spaces. The theory was originally developed by M. Gromov in his book Metric Structures for Riemannian and Non-Riemannian Spaces and based on the idea of the concentration of measure phenomenon by Lévy and Milman. A central theme in this book is the study of the observable distance between metric measure spaces, defined by the difference between 1-Lipschitz functions on one space and those on the other. The topology on the set of metric measure spaces induced by the observable distance function is weaker than the measured Gromov–Hausdorff topology and allows the author to investigate a sequence of Riemannian manifolds with unbounded dimensions.

One of the main parts of this presentation is the discussion of a natural compactification of the completion of the space of metric measure spaces. The stability of the curvature-dimension condition is also discussed.

A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in metric measure spaces.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.