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Pure Metric Geometry

  • Book
  • © 2023

Overview

Authors:
  1. Anton Petrunin

    1. Department of Mathematics, Pennsylvania State University, University Park, USA

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  • Lectures provide a valuable resource for graduate students in mathematics and advanced undergraduate students
  • Provides a concise introduction to key constructions in metric geometry
  • Illustrates key topics, including Urysohn's universal space, injective spaces, and ultralimits

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-viii
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  2. Definitions

    • Anton Petrunin
    Pages 1-13

  3. Universal Spaces

    • Anton Petrunin
    Pages 15-24

  4. Injective Spaces

    • Anton Petrunin
    Pages 25-35

  5. Space of Subsets

    • Anton Petrunin
    Pages 37-42

  6. Space of Spaces

    • Anton Petrunin
    Pages 43-54

  7. Ultralimits

    • Anton Petrunin
    Pages 55-63

  8. Back Matter

    Pages 65-103
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Keywords

About this book

This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an analysis of universal spaces, injective spaces, the Gromov-Hausdorff convergence, and ultralimits. This book illustrates basic examples of domestic affairs of metric spaces, this includes Alexandrov geometry, geometric group theory, metric-measure spaces and optimal transport.

Researchers in metric geometry will find this book appealing and helpful, in addition to graduate students in mathematics, and advanced undergraduate students in need of an introduction to metric geometry. Any previous knowledge of classical geometry, differential geometry, topology, and real analysis will be useful in understanding the presented topics. 

Authors and Affiliations

  • Department of Mathematics, Pennsylvania State University, University Park, USA

    Anton Petrunin

About the author

Anton Petrunin is Professor of Mathematics at Penn State.

Bibliographic Information

  • Book Title: Pure Metric Geometry

  • Authors: Anton Petrunin

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-39162-0

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Softcover ISBN: 978-3-031-39161-3Published: 22 November 2023

  • eBook ISBN: 978-3-031-39162-0Published: 21 November 2023

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: VIII, 103

  • Number of Illustrations: 17 b/w illustrations

  • Topics: Geometry

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