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 Dave Auckly - arXiv
This paper introduced undergraduates to the Atiyah-Singer index theorem. It includes a statement of the theorem, an outline of the easy part of the heat equation proof. It includes counting lattice points and knot concordance as applications.
by M. Kuranishi - Tata Institute of Fundamental Research
Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.
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 Dominic Joyce - arXiv
An introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture.