Some inequalities for the Poincaré metric of plane domains

DOI10.1007/s00209-005-0782-0zbMath1081.30040OpenAlexW1974445853MaRDI QIDQ2574922

Toshiyuki Sugawa, Matti Vuorinen

Publication date: 5 December 2005

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: http://ir.lib.hiroshima-u.ac.jp/files/public/1/17233/20141016130733740904/MZ_250_885.pdf

zbMATH Keywords

hyperbolic metricPoincaré metricLittlewood's Theorem

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Inequalities in the complex plane (30A10)

Related Items (21)

Intrinsic geometry and boundary structure of plane domains ⋮ Generalized two-field \(\alpha\)-attractor models from the hyperbolic triply-punctured sphere ⋮ Generalized \(\alpha\)-attractor models from elementary hyperbolic surfaces ⋮ Hypergeometric functions and hyperbolic metric ⋮ Estimates of the hyperbolic metric on the twice punctured plane ⋮ Construction of nearly hyperbolic distance on punctured spheres ⋮ A conformal invariant for nonvanishing analytic functions and its applications ⋮ Turán type inequalities for generalized complete elliptic integrals ⋮ Boundary asymptotics of the relative Bergman kernel metric for elliptic curves III: 1 & ∞ ⋮ The spherical metric and univalent harmonic mappings ⋮ Möbius invariant metrics bilipschitz equivalent to the hyperbolic metric ⋮ Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves ⋮ On the hyperbolic distance of \(n\)-times punctured spheres ⋮ Strong submultiplicativity of the Poincaré metric ⋮ Estimation of the hyperbolic metric by using the punctured plane ⋮ On fixed-points and singular values of transcendental meromorphic functions ⋮ Twice-punctured hyperbolic sphere with a conical singularity and generalized elliptic integral ⋮ Topics in special functions. II ⋮ Boundary asymptotics of the relative Bergman kernel metric for elliptic curves II: subleading terms ⋮ An estimate of the maximal dilatations of quasiconformal automorphisms of annuli ⋮ Hyperbolic distance versus quasihyperbolic distance in plane domains

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• Precise Bounds in the Theorems of Schottky and Picard
• On Explicit Bounds in Landau's Theorem. II
• The Poincaré Metric of Plane Domains
• Uniformly Perfect Sets and Quasiregular Mappings
• Uniformly perfect sets and distortion of holomorphic functions
• Angles and Quasiconformal Mappings^†
• Comparing invariant distances and conformal metrics on Riemann surfaces
• Estimates for the hyperbolic metric of the punctured plane and applications
• Comparing Poincaré densities

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