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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie An Invitation to Alexandrov Geometry: CAT(0) Spaces
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An Invitation to Alexandrov Geometry: CAT(0) Spaces
Stephanie Alexander, Vitali Kapovitch, Anton Petrunin (Broschiert, Englisch)
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Beschreibung
This volume discusses CAT(0) spaces – metric spaces with nonpositive curvature in the sense of Alexandrov – which may be viewed as a non-linear generalization of Hilbert spaces. The book showcases the beauty and power of Alexandrov geometry by reaching interesting applications and theorems with a minimum of preparation. This thoroughly revised and updated edition expands the 2019 SpringerBriefs in… Mathematics volume. Drawing on extensive teaching experience, the authors have added two major topics, introduced numerous new exercises, corrected errors, simplified several proofs, and reorganized the material to better support teaching needs. The presentation is now more accessible and elementary. Primarily intended for graduate students and motivated undergraduates, the book includes numerous exercises ranging from routine to advanced, together with “semisolutions” and hints. It is well suited for self-study by advanced undergraduates, graduate students, and researchers. From the reviews of the first edition: "In the preface of this book, the authors state a “Manifesto of Alexandrov geometry”, under the slogan “back to Euclid”: Alexandrov geometry may be viewed as a direct generalization of the axiomatic system of Euclid, with some of the equalities changed to inequalities. Indeed, metric geometry permits to formulate curvature bounds merely in terms of distance relations, e.g. via triangle comparison. This monograph is a brief and well crafted introduction into this highly active field. [...] Throughout the text there are numerous exercises of varying difficulty, as well as hints for the solutions in a separate section called “Semisolutions”. This book is a pleasure to read and is highly recommended as a concise and stimulating introduction to metric geometry." Monatshefte für Mathematik 2021 Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
23.08.2026
Sprache
Englisch
EAN
9783032253484
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Lecture Notes in Mathematics
Sonderedition
Nein
Autor
Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
Seitenanzahl
115
Auflage
2
Einbandart
Broschiert
Schlagwörter
Alexandrov geometry, CAT(0), CAT(k), nonpositive curvature, Reshetnyak gluing theorem, Hadamard–Cartan theorem, globalization, barycenters in metric geometry, polyhedral spaces, spaces with curvature bounded above, exotic aspherical manifolds
Thema-Inhalt
PBMP - Differentielle und Riemannsche Geometrie
PBG - Gruppen und Gruppentheorie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Switzerland AG, Europaplatz 3,69115 Heidelberg, Germany, Heidelberg, Deutschland, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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