Pure metric geometry

Anton Petrunin (Autor)

Buch | Softcover

VIII, 103 Seiten

2023 | 1. Auflage
Springer International Publishing (Verlag)
978-3-031-39161-3 (ISBN)

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lt;p>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.

lt;p>Anton Petrunin is Professor of Mathematics at Penn State.

1 Definitions. - A. Metric spaces. -B. Topology. - C. Variations. -D. Maximal metric and gluing. - E. Completeness. -F. Compact spaces. - G. Proper spaces. -H. Geodesics. - I. Metric trees. - J. Length. - K. Length spaces. - 2 Universal spaces. - A. Embedding in a normed space. - B. Extension property. - C. Universality. - D. Uniqueness and homogeneity. - E. Remarks. - 3 Injective spaces. - A. Definition. - B. Admissible and extremal functions. - C. Equivalent conditions. - D. Space of extremal functions. - E. Injective envelope. - F. Remarks. - 4 Space of subsets. - A. Hausdorff distance. -B. Hausdorff convergence. - C. An application. -D. Remarks. - 5 Space of spaces. - A. Gromov-Hausdorff metric. - B. Approximations and almost isometries 49; C. Optimal realization 50; D. Convergence 51; E. Uniformly totally bonded families 52; F. Gromov selection theorem. - G. Universal ambient space. - H. Remarks. - 6 Ultralimits. - A. Faces of ultrafilters. - B. Ultralimits of points. - C. An illustration. - D. Ultralimits of spaces. - E. Ultrapower. - F. Tangent and asymptotic spaces. - G. Remarks. - Semisolutions. -Index. - Bibliography

Erscheinungsdatum	22.11.2023
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	Illustrationen
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	183 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	geodesics • Gromov-Hausdorff convergence • Gromov Selection Theorem • hausdorff distance • Injective Spaces • Metric Trees • Ultralimits • Universal Ambient Space • Universal Spaces
ISBN-10	3-031-39161-6 / 3031391616
ISBN-13	978-3-031-39161-3 / 9783031391613
Zustand	Neuware