Hyperbolic Complex Spaces
In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.
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Holomorphic Maps into Hyperbolic Spaces
Extension and Finiteness Theorems
Complex Finsler Vector Bundles
Manifolds of General Type
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algebraic ample apply assume boundary bounded Chapter closed compact complex space complete hyperbolic complex manifold complex space complex subspace component condition connected consider constant contained continuous converges coordinate system Corollary curvature curve defined definition denote differential dimension disc distance divisor domain element equality example exists extends f e Hol(D fact fiber field finite fixed function given hand Hence Hermitian Hol(X holomorphic map hyperbolically imbedded hyperplane implies induces inequality integer irreducible Lemma length length function Let X line bundle linear map f Math metric modulo natural negative neighborhood nonsingular normal obtain origin particular positive projective Proof Proposition prove pseudo-distance relatively compact respect result satisfies sequence singularities structure subsequence subset tangent taut Theorem vector zero