The Schwarz lemma

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Clarendon Press, Jan 1, 1990 - Mathematics - 248 pages
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This volume reflects the profound impact of the century-old Schwarz lemma on contemporary complex variable theory and functional analysis. The underlying theme is the theory of intrinsic metrics on complex manifolds in finite and infinite dimensions, with reports on recent developments. In addition to full treatment of classical results and the Schwarz lemma for subharmonic and plurisubharmonic functions, the author examines Schwarz-pick systems, hyperbolic manifolds, special domains, infinitesimal metric, holomorphic curvature, the algebraic-geometric of Harris, and differential-geometric, algebraic-geometric, and fixed-point free versions of the Schwarz lemma. This self-contained text provides a synthesis of knowledge in an area of growing interest.

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The classical Schwarz lemma
A Schwarz lemma for plurisubharmonic functions 20
The Poincare distance on the unit disc

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