The Harnack and other conformally invariant metrics

DOI10.2996/kmj/1138037356zbMath0631.31001OpenAlexW1968658431MaRDI QIDQ1094555

David A. Herron

Publication date: 1987

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2996/kmj/1138037356

zbMATH Keywords

quasihyperbolic metrichyperbolic metricsharp upper boundconformally invariant metricsCaratheodory metricPoincaré metricsconformally inariant pseudo-distancesHarnack metricinfinitesimal form

Mathematics Subject Classification ID

Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05)

Related Items (3)

Conformal invariants defined by harmonic functions on Riemann surfaces ⋮ Separation of points by classes of harmonic functions ⋮ Comparing invariant distances and conformal metrics on Riemann surfaces

Cites Work

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• The sub-mean-value property of subharmonic functions and its application to the estimation of the Gaussian curvature of the span metric
• Schwarzian derivatives, the Poincaré metric and the kernel function
• Quasiconformally homogeneous domains
• On Harnack's pseudo-distance
• Die Harnacksche Metrik in der Theorie der harmonischen Funktionen
• Bounded analytic functions
• Confromal invariants and function-theoretic null-sets
• On a distance invariant under Möbius transformations in R^n
• On the Harnack constant and the boundary behavior of Harnack functions
• The Caratheodory Metric of the Annulus
• On constants in extremal problems of analytic functions

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