by Karsten Grove, Peter Petersen
Publisher: Cambridge University Press 1997
Number of pages: 262
Comparison Geometry asks: What can we say about a Riemannian manifold if we know a bound for its curvature, and perhaps something about its topology? This volume is an up-to-date panorama of Comparison Geometry, featuring surveys and new research. Surveys present classical and recent results, and often include complete proofs, in some cases involving a new and unified approach. The historical evolution of the subject is summarized in charts and tables of examples.
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by Paul Loya - Binghamton University
This is a lecture-based class on the Atiyah-Singer index theorem, proved in the 60's by Sir Michael Atiyah and Isadore Singer. Their work on this theorem lead to a joint Abel prize in 2004. Requirements: Knowledge of topology and manifolds.
by Stefan Waldmann - arXiv
We discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed.
by Gerhard Knieper, Norbert Peyerimhoff - arXiv
We provide a survey on recent results on noncompact simply connected harmonic manifolds, and we also prove many new results, both for general noncompact harmonic manifolds and for noncompact harmonic manifolds with purely exponential volume growth.
by Mark Pinsky, Bjorn Birnir - Cambridge University Press
The three main themes of this book are probability theory, differential geometry, and the theory of integrable systems. The papers included here demonstrate a wide variety of techniques that have been developed to solve various mathematical problems.