Download The Schwarz Lemma (Dover Books on Mathematics) by Sean Dineen PDF

By Sean Dineen

The Schwarz lemma is likely one of the easiest ends up in advanced research that trap the tension of holomorphic features. This self-contained quantity presents an intensive assessment of the topic; it assumes no wisdom of intrinsic metrics and goals for the most effects, introducing notation, secondary options, and strategies as beneficial. compatible for complicated undergraduates and graduate scholars of arithmetic, the two-part therapy covers uncomplicated idea and purposes.
Starting with an exploration of the topic by way of holomorphic and subharmonic services, the therapy proves a Schwarz lemma for plurisubharmonic services and discusses the elemental homes of the Poincaré distance and the Schwarz-Pick structures of pseudodistances. extra themes comprise hyperbolic manifolds, distinct domain names, pseudometrics outlined utilizing the (complex) eco-friendly functionality, holomorphic curvature, and the algebraic metric of Harris. the second one half explores mounted element theorems and the analytic Radon-Nikodym property.

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