On variational principles of conformal mappings

DOI10.1090/S1061-0022-07-00955-7zbMath1146.30011OpenAlexW2039673301MaRDI QIDQ5442117

V. N. Dubinin, Elena G. Prilepkina

Publication date: 15 February 2008

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-07-00955-7

zbMATH Keywords

symmetrizationpolarizationunivalent functionsRobin functionRobin capacitydistorsion theoremscapacity of a condensermajorant domains

Mathematics Subject Classification ID

General theory of conformal mappings (30C35) Extremal problems for conformal and quasiconformal mappings, variational methods (30C70)

Related Items (2)

Holomorphic mappings of a strip into itself with bounded distortion at infinity ⋮ On I. P. Mityuk's results on the behavior of the inner radius of a domain and the condenser capacity under regular mappings

Cites Work

• On the computation of modules of long quadrilaterals
• On conformal moduli of polygonal quadrilaterals
• Generalized condensers and the asymptotics of their capacities under degeneration of some plates
• Radial averaging of domains, estimates for Dirichlet integrals and applications
• Distortion of the hyperbolic Robin capacity under a conformal mapping and extremal configurations
• The Schwarz inequality on the boundary for functions regular in the disk
• Robin functions and energy functionals of multiply connected domains
• Symmetrization and univalent functions in an annulus
• Extremal domains for robin capacity
• Robin Capacity and Lift of Infinitely Thin Airfoils
• Robin functions and distortion of capacity under conformal mapping
• A Representation Formula for the Robin Function
• Robin's Modulus in a Hele-Shaw Problem
• Concentration of area in half-planes
• Local variations and minimal area problem for Caratheodory functions
• Schwarz's lemma and estimates of coefficients for regular functions with free domain of definition
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
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