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

Autorentext

Anton Petrunin is Professor of Mathematics at Penn State.

Inhalt

Preface.- Definitions.- Universal Spaces.- Injective Spaces.- Space of Subsets.- Space of Spaces.- Ultralimits.- Semisolutions.- Bibliography.