Geometric versions of Schwarz's lemma and symmetrization

DOI10.1007/s10958-011-0542-0zbMath1304.30035OpenAlexW2133518922WikidataQ124856736 ScholiaQ124856736MaRDI QIDQ476651

V. N. Dubinin

Publication date: 2 December 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-011-0542-0

zbMATH Keywords

Schwarz's lemmasymmetrization principle

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 (7)

Growth theorems for holomorphic functions under geometric conditions for the image ⋮ Geometric versions of Schwarz’s lemma for spherically convex functions ⋮ On the images of horodisks under holomorphic self-maps of the unit disk ⋮ Upper and lower estimates for the modulus of bounded holomorphic functions ⋮ Growth and monotonicity properties for elliptically schlicht functions ⋮ Multi-point bounds for analytic functions under measure conditions ⋮ Hyperbolic geometric versions of Schwarz’s lemma

Cites Work

• Hyperbolic transfinite diameter and some theorems on analytic functions in an annulus
• Some inequalities for the capacity of plane condensers
• Transformations of domains in the plane and applications in the theory of functions
• Length and area estimates for analytic functions
• Geometric versions of Schwarz’s lemma for quasiregular mappings
• Julius and Julia: Mastering the Art of the Schwarz Lemma
• A Schwarz lemma for meromorphic functions and estimates for the hyperbolic metric
• Area, capacity and diameter versions of Schwarz’s Lemma
• Symmetrization in the geometric theory of functions of a complex variable
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