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- Schwarz–Ahlfors–Pick_theorem abstract "In mathematics, the Schwarz–Ahlfors–Pick theorem is an extension of the Schwarz lemma for hyperbolic geometry, such as the Poincaré half-plane model.The Schwarz–Pick lemma states that every holomorphic function from the unit disk U to itself, or from the upper half-plane H to itself, will not increase the Poincaré distance between points. The unit disk U with the Poincaré metric has negative Gaussian curvature -1. In 1938, Lars Ahlfors generalised the lemma to maps from the unit disk to other negatively curved surfaces:Theorem (Schwarz–Ahlfors–Pick). Let U be the unit disk with Poincaré metric let S be a Riemann surface endowed with a Hermitian metric whose Gaussian curvature is ≤ −1; let be a holomorphic function. Then for all A generalization of this theorem was proved by Shing-Tung Yau in 1973.".
- Schwarz–Ahlfors–Pick_theorem wikiPageID "1487910".
- Schwarz–Ahlfors–Pick_theorem wikiPageRevisionID "551260117".
- Schwarz–Ahlfors–Pick_theorem subject Category:Hyperbolic_geometry.
- Schwarz–Ahlfors–Pick_theorem subject Category:Riemann_surfaces.
- Schwarz–Ahlfors–Pick_theorem subject Category:Theorems_in_complex_analysis.
- Schwarz–Ahlfors–Pick_theorem subject Category:Theorems_in_differential_geometry.
- Schwarz–Ahlfors–Pick_theorem comment "In mathematics, the Schwarz–Ahlfors–Pick theorem is an extension of the Schwarz lemma for hyperbolic geometry, such as the Poincaré half-plane model.The Schwarz–Pick lemma states that every holomorphic function from the unit disk U to itself, or from the upper half-plane H to itself, will not increase the Poincaré distance between points. The unit disk U with the Poincaré metric has negative Gaussian curvature -1.".
- Schwarz–Ahlfors–Pick_theorem label "Lemma von Schwarz-Pick".
- Schwarz–Ahlfors–Pick_theorem label "Schwarz–Ahlfors–Pick theorem".
- Schwarz–Ahlfors–Pick_theorem label "Теорема Пика (комплексный анализ)".
- Schwarz–Ahlfors–Pick_theorem sameAs Schwarz%E2%80%93Ahlfors%E2%80%93Pick_theorem.
- Schwarz–Ahlfors–Pick_theorem sameAs Lemma_von_Schwarz-Pick.
- Schwarz–Ahlfors–Pick_theorem sameAs Q942046.
- Schwarz–Ahlfors–Pick_theorem sameAs Q942046.
- Schwarz–Ahlfors–Pick_theorem wasDerivedFrom Schwarz–Ahlfors–Pick_theorem?oldid=551260117.