An invitation to Alexandrov geometry : CAT(0) spaces /: CAT(0) spaces. ([2019])

• Record Type: Book
• Further Information: Note: Stephanie Alexander, Vitali Kapovitch, Anton Petrunin.
• Authors: Alexander, Stephanie; Kapovitch, Vitali; Petrunin, Anton
• Contents: Intro; Preface; Early history of Alexandov geometry; Manifesto of Alexandrov geometry; Acknowledgements; Contents; 1 Preliminaries; 1.1 Metric spaces; 1.2 Constructions; 1.3 Geodesics, triangles, and hinges; 1.4 Length spaces; 1.5 Model angles and triangles; 1.6 Angles and the first variation; 1.7 Space of directions and tangent space; 1.8 Hausdorff convergence; 1.9 Gromov-Hausdorff convergence; 2 Gluing theorem and billiards; 2.1 The 4-point condition; 2.2 Thin triangles; 2.3 Reshetnyak's gluing theorem; 2.4 Reshetnyak puff pastry; 2.5 Wide corners; 2.6 Billiards; 2.7 Comments 3 Globalization and asphericity3.1 Locally CAT spaces; 3.2 Space of local geodesic paths; 3.3 Globalization; 3.4 Polyhedral spaces; 3.5 Flag complexes; 3.6 Cubical complexes; 3.7 Exotic aspherical manifolds; 3.8 Comments; 4 Subsets; 4.1 Motivating examples; 4.2 Two-convexity; 4.3 Sets with smooth boundary; 4.4 Open plane sets; 4.5 Shefel's theorem; 4.6 Polyhedral case; 4.7 Two-convex hulls; 4.8 Proof of Shefel's theorem; 4.9 Comments; Semisolutions; References; ; Index
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 516.373; Generalized spaces; Riemannian manifolds; Geometry, Riemannian; MATHEMATICS / Geometry / General; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030053123; 3030053121
• Related ISBNs: 9783030053116
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed May 10, 2019).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.