Geometric versions of Schwarz’s lemma for quasiregular mappings

DOI10.1090/S0002-9939-2010-10604-4zbMath1217.30021OpenAlexW1965621061WikidataQ124964102 ScholiaQ124964102MaRDI QIDQ2997197

Dimitrios Betsakos

Publication date: 6 May 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2010-10604-4

zbMATH Keywords

Schwarz lemmacapacityquasiregular mappingextremal lengthconformal modulus

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80)

Related Items (16)

Conformal modulus and its reduction via mean curvatures ⋮ Length and area estimates for (hyperbolically) convex conformal mappings ⋮ Conformal mapping, convexity and total absolute curvature ⋮ Isoperimetric properties of condenser capacity ⋮ Geometric versions of Schwarz’s lemma for spherically convex functions ⋮ Two isoperimetric inequalities for the Sobolev constant ⋮ Geometric versions of Schwarz's lemma and symmetrization ⋮ Isometries for the modulus metric in higher dimensions are conformal mappings ⋮ Upper and lower estimates for the modulus of bounded holomorphic functions ⋮ Geometrical logarithmic capacitance ⋮ Isoperimetry for semilinear torsion problems in Riemannian two-manifolds ⋮ Multi-point variations of the Schwarz lemma with diameter and width conditions ⋮ Hyperbolic geometric versions of Schwarz’s lemma ⋮ On the variational \(p\)-capacity problem in the plane ⋮ The Schwarz Lemma: Rigidity and Dynamics ⋮ On the duration of stays of Brownian motion in domains in Euclidean space

Cites Work

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• Precise estimate of the 2-capacity of a condenser
• Conformal geometry and quasiregular mappings
• Integral means, univalent functions and circular symmetrization
• Lectures on \(n\)-dimensional quasiconformal mappings
• Moduli in Modern Mapping Theory
• Area, capacity and diameter versions of Schwarz’s Lemma
• Dimension-Free Quasiconformal Distortion in n-Space

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