Schwarz Ahlfors Pick Theorem
Versandkostenfrei!
Versandfertig in 6-10 Tagen
19,99 €
inkl. MwSt.
PAYBACK Punkte
10 °P sammeln!
High Quality Content by WIKIPEDIA articles! In mathematics, the Schwarz Ahlfors Pick theorem is an extension of the Schwarz lemma for hyperbolic geometry, such as the Poincaré half-plane model. It states that the Poincaré metric is distance-decreasing on harmonic functions. The theorem states that every holomorphic function on the unit disk U, or the upper half-plane H, with distances defined by the Poincaré metric, is a contraction mapping. That is, every such analytic mapping will not increase the distance between points. Stated more precisely: Theorem: (Schwarz Ahlfors Pick) For all holo...
High Quality Content by WIKIPEDIA articles! In mathematics, the Schwarz Ahlfors Pick theorem is an extension of the Schwarz lemma for hyperbolic geometry, such as the Poincaré half-plane model. It states that the Poincaré metric is distance-decreasing on harmonic functions. The theorem states that every holomorphic function on the unit disk U, or the upper half-plane H, with distances defined by the Poincaré metric, is a contraction mapping. That is, every such analytic mapping will not increase the distance between points. Stated more precisely: Theorem: (Schwarz Ahlfors Pick) For all holomorphic functions f:Urightarrow U, one has rho(f(z_1),f(z_2)) leq rho(z_1,z_2) for points z_1,z_2 in U and Poincaré distance . For any tangent vector T, the hyperbolic length of the tangent vector does not increase: f^ (T) leq T .
Andere Kunden interessierten sich für
