Overview

The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date. This volume of lecture notes focuses on its differential geometric developments by several excellent authors including, but not limited to, L Ahlfors, S S Chern, Y C Lu, S T Yau and H L Royden.This volume can be approached by a reader who has basic knowledge on complex analysis and Riemannian geometry. It contains major historic differential geometric generalizations on Schwarz's Lemma and provides the necessary information while making the whole volume as concise as ever.Contents: Some FundamentalsClassical Schwarz's Lemma and the Poincaré MetricAhlfors' GeneralizationFundamentals of Hermitian and Kählerian GeometryChern–Lu FormulaTamed Exhaustion and Almost Maximum PrincipleGeneral Schwarz's Lemma by Yau and RoydenMore Recent DevelopmentsReadership: Graduate students and researchers in complex analysis, differential geometrics and Riemannian geometry.

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9781283145169

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