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From Follett
Partial differential equations related to the Gauss-Bonnet-Chern integrand on 4-manifolds / Sun-Yung A. Chang and Paul C. Yang -- http://www.ams.org/ulect/027 http://dx.doi.org/10.1090/ulect/027/01 Geometry of, and via, symmetries / Karsten Grove -- http://www.ams.org/ulect/027 http://dx.doi.org/10.1090/ulect/027/02 Lagrangian cycles and volume / Jon G. Wolfson -- http://www.ams.org/ulect/027 http://dx.doi.org/10.1090/ulect/027/03 Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactifications of manifolds and on Yamabe-type variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially in connection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus of variations. The lectures provide an up-do-date overview and an introduction to the research literature in each of their areas. This very readable introduction should prove useful to graduate students and researchers in differential geometry and geometric analysis.
From the Publisher
Three surveys introduce the background, context, and main techniques of recent developments in three distinct areas of differential geometry--conformally invariant curvatures and operators in four dimensions, the use of isometric group actions and metric geometry techniques to understand examples and the classification of Riemannian manifolds, and variational problems for Lagrangian immersions in symplectic manifolds. No index. Annotation copyrighted by Book News, Inc., Portland, OR