Pure Metric Geometry
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Beschreibung
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.
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
Autor*in
Anton Petrunin
Themen in »Pure Metric Geometry«
Universal Spaces Injective Spaces Gromov-Hausdorff Convergence Metric Trees Hausdorff Distance Ultralimits Geodesics Gromov Selection Theorem Universal Ambient Space
Stimmen zu »Pure Metric Geometry«
“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)
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