ENGLISH

Metric Measure Geometry: Gromov's Theory of Convergence and Concentration of Metrics and Measures

By Takashi Shioya

Book information

Publisher
European Mathematical Society
Year
2016
ISBN
3037191589, 9783037191583
Language
english
Format
PDF
Filesize
1 MB (1106802 bytes)
Series
IRMA Lectures in Mathematics & Theoretical Physics
Pages
196\196
Time added
2016-01-18 16:46:20
Differential Geometry Topology Mathematics Science

Description

This book studies a new theory of metric geometry on metric measure spaces, 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 due to Lévy and Milman. A central theme in this text 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 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.This book makes advanced material accessible to researchers and graduate students interested in metric measure spaces.

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