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Aimed toward graduate students and research mathematicians, with
minimal prerequisites this book provides a fresh take on Alexandrov
geometry and explains the importance of CAT(0) geometry in
geometric group theory. Beginning with an overview of fundamentals,
definitions, and conventions, this book quickly moves forward to
discuss the Reshetnyak gluing theorem and applies it to the
billiards problems. The Hadamard-Cartan globalization theorem is
explored and applied to construct exotic aspherical manifolds.
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.Â
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