The Schwarz LemmaThis 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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analytic arbitrary aRNP Aut(D Banach manifold Banach space biholomorphically equivalent bounded domain bounded symmetric domains Carathéodory chapter complex Banach manifold complex C-geodesic complex manifold converges convex bounded convex domain Corollary D₁ D¹(M D₂ defined definition denote distance extreme point finite dimensional finite rank Finsler metric Fix ƒ geodesic Green function Hence Hermitian metric Hilbert space holomorphic curvature holomorphic functions holomorphic mappings holomorphic retract implies inequality infinite inner product intrinsic metrics invariant irreducible isometrically isomorphic J. P. Vigué Kaup lim sup linear mapping Math minimal tripotents neighbourhood norm open unit ball plurisubharmonic functions positive integer properties proposition proved pseudoconvex pseudodistance pseudometric PSH(D real numbers result Schwarz lemma Schwarz-Pick lemma Schwarz-Pick system sequence shows subharmonic submanifold subspace suppose theory topology triple system unique unit ball upper semicontinuous Vesentini