This book is a compendium of survey lectures presented at a conference on Riemannian Geometry sponsored by The Fields Institute for Research in Mathematical Sciences (Waterloo, Canada) in August 1993. Attended by over 80 participants, the aim of the conference was to promote research activity in Riemannian geometry. A select group of internationally established researchers in the field were invited to discuss and present current developments in a selection of contemporary topics in Riemannian geometry. This volume contains four of the five survey lectures presented at the conference. The book features basic notions of volume and entropy and the difficult and deep relations of these invariants to curvature. It also features $LP$ cohomology, in which the methods combine various areas of mathematics going beyond Riemannian geometry. It covers curvature inequalities from a general point of view, leading to the study of general spaces.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
Gewicht
ISBN-13
978-0-8218-0263-2 (9780821802632)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
Lecture Series 1. Gerard Besson, Volumes and entropies Preface Volumes Simplicial volume Entropies Some results and a new method Biblography Lecture Series 2. Joachim Lohkamp, Global and local curvatures Preface Curved balls Approximation Internal structures Bibliography Lecture Series 3. Pierre Pansu, Introduction to $L^2$ Betti numbers Acknowledgments Introduction Von-Neumann dimension Simplicial $L^2$ Betti numbers Homotopy invariance Invariants of discrete groups Atiyah's $L^2$ index theorem $L^\infty$ cohomology and negative curvature A vanishing theorem for Kahler hyperbolic manifolds Non vanishing theorems for $L^2$ cohomology $L^2$ index for projectively invariant operators Lecture Series 4. Peter Petersen, Comparison geometry problem list Bibliography Introduction Review of techniques in comparison theory Results in comparison geometry Problems Bibliograpy.
