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

By Sean Dineen

The Schwarz lemma is one of the easiest leads to complicated research that seize the tension of holomorphic capabilities. This self-contained quantity presents an intensive review of the topic; it assumes no wisdom of intrinsic metrics and goals for the most effects, introducing notation, secondary innovations, and strategies as priceless. compatible for complex undergraduates and graduate scholars of arithmetic, the two-part remedy covers simple thought and purposes.
Starting with an exploration of the topic when it comes to holomorphic and subharmonic services, the therapy proves a Schwarz lemma for plurisubharmonic services and discusses the elemental houses of the Poincaré distance and the Schwarz-Pick platforms of pseudodistances. extra issues contain hyperbolic manifolds, specified 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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