Growth theorems for holomorphic functions under geometric conditions for the image

DOI10.1007/s40315-013-0021-3zbMath1283.30056OpenAlexW2143521550MaRDI QIDQ380723

Galatia Cleanthous

Publication date: 14 November 2013

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40315-013-0021-3

zbMATH Keywords

Schwarz lemmapolarizationGreen functionhyperbolic metriclogarithmic capacitycircular symmetrizationSteiner symmetrizationcondenser capacitymodulus metric

Mathematics Subject Classification ID

Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80) Capacity and harmonic measure in the complex plane (30C85) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (3)

Bounded holomorphic functions covering no concentric circles ⋮ Growth and monotonicity properties for elliptically schlicht functions ⋮ Multi-point bounds for analytic functions under measure conditions

Cites Work

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• Geometric versions of Schwarz's lemma and symmetrization
• Symmetrization and the Poincaré metric
• Conformal geometry and quasiregular mappings
• On the distribution of values of meromorphic functions of bounded characteristic
• HOLOMORPHIC FUNCTIONS WITH IMAGE OF GIVEN LOGARITHMIC OR ELLIPTIC CAPACITY
• Multi-point variations of the Schwarz lemma with diameter and width conditions
• Monotonicity theorems for analytic functions centered at infinity
• A Schwarz lemma for meromorphic functions and estimates for the hyperbolic metric
• Area, capacity and diameter versions of Schwarz’s Lemma
• Versions of Schwarz's Lemma for Condenser Capacity and Inner Radius
• Conformal Metrics
• Weighted Integral Means of Mixed Areas and Lengths Under Holomorphic Mappings

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