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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.
List of contents
Preface.- Definitions.- Universal Spaces.- Injective Spaces.- Space of Subsets.- Space of Spaces.- Ultralimits.- Semisolutions.- Bibliography.
About the author
Anton Petrunin is Professor of Mathematics at Penn State.
Report
"This is a succinct introduction to the tools one needs to understand metric geometry. It starts with the most basic definitions ... to move on to more advanced topics ... . There are exercises of various levels of difficulty with 'semisolutions' at the back of the book. For complicated solutions, the source of the solution in the literature is also mentioned." (Victor V. Pambuccian, zbMATH 1541.54001, 2024)
