Metric Structures for Riemannian and Non-Riemannian Spaces

• Κύριος συγγραφέας: Gromov, Mikhail (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston, MA : Birkhäuser Boston, 2007.
• Σειρά: Modern Birkhäuser Classics
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Measure theory.; Differential geometry.; Algebraic topology.; Manifolds (Mathematics).; Complex manifolds.; Differential Geometry.; Manifolds and Cell Complexes (incl. Diff.Topology).; Algebraic Topology.; Measure and Integration.; Analysis.

Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave began with seminal papers by Svarc and Milnor on...

Πίνακας περιεχομένων:

• Preface to the French Edition
• Preface to the English Edition
• Introduction: Metrics Everywhere
• Length Structures: Path Metric Spaces
• Degree and Dilatation
• Metric Structures on Families of Metric Spaces
• Convergence and Concentration of Metrics and Measures
• Loewner Rediscovered
• Manifolds with Bounded Ricci Curvature
• Isoperimetric Inequalities and Amenability
• Morse Theory and Minimal Models
• Pinching and Collapse
• Appendix A: 'Quasiconvex' Domains in Rn
• Appendix B: Metric Spaces and Mappings Seen at Many Scales
• Appendix C: Paul Levy's Isoperimetric Inequality
• Appendix D: Systolically Free Manifolds
• Bibliography
• Glossary of Notation
• Index.