On Grunsky operator

DOI10.1007/s11425-007-0141-1zbMath1138.30305OpenAlexW2076593748MaRDI QIDQ2475329

Yuliang Shen

Publication date: 11 March 2008

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-007-0141-1

zbMATH Keywords

univalent functioncompact operatorquasiconformal mappingHilbert-Schmidt operator

Mathematics Subject Classification ID

Linear operators defined by compactness properties (47B07) Quasiconformal mappings in the complex plane (30C62) General theory of univalent and multivalent functions of one complex variable (30C55)

Related Items (16)

Dirichlet spaces of domains bounded by quasicircles ⋮ On the compactness of Grunsky differential operators ⋮ The Loewner–Kufarev energy and foliations by Weil–Petersson quasicircles ⋮ Generalized Fourier coefficients of a quasisymmetric homeomorphism and the Fredholm eigenvalue ⋮ The cross-ratio distortion of integrably asymptotic affine homeomorphism of unit circle ⋮ Analysis on quasidisks: a unified approach through transmission and jump problems ⋮ On Grunsky inequalities and the exact domain of variability of the Grunsky functional ⋮ Comparison Moduli Spaces of Riemann Surfaces ⋮ Faber and Grunsky operators corresponding to bordered Riemann surfaces ⋮ Quasiconformal Teichmüller theory as an analytical foundation for two-dimensional conformal field theory ⋮ On quasisymmetric homeomorphisms ⋮ Holomorphic contractibility and other properties of the Weil-Petersson and VMOA Teichmüller spaces ⋮ Integrable Teichmüller space ⋮ Dirichlet problem and Sokhotski-Plemelj jump formula on Weil-Petersson class quasidisks ⋮ The universal Teichmüller space and function space ⋮ Faber polynomials with applications to univalent functions with quasiconformal extensions

Cites Work

• Holomorphic functions of several variables. An introduction to the fundamental theory. With the assist. of Gottfried Barthel transl. by Michael Bridgland
• Grunsky coefficient inequalities, Carathéodory metric and extremal quasiconformal mappings
• Diff(S\({}^ 1)\) and the Teichmüller spaces
• Polygonal quasiconformal maps and Grunsky inequalities
• Characterization of quasi-disks and Teichmüller spaces
• On analytic and geometric properties of Teichmüller spaces
• The Grunsky coefficient conditions
• Grunsky's inequality and its applications to Teichmüller spaces
• Integrably asymptotic affine homeomorphisms of the circle and Teichmüller spaces
• Teichmüller theory and the universal period mapping via quantum calculus and the \(H^{1/2}\) space on the circle
• The Velling-Kirillov metric of the universal Teichmüller curve
• Quasiconformal extremals of non-regular functionals
• Invariant metrics on Teichmüller spaces and quasiconformal extendability of analytic functions
• A period mapping in universal Teichm\"uller space
• Symmetric Structures on a Closed Curve
• On the Tangent Space to the Universal Teichmuller Space
• The holomorphic contractibility of two generalized Teichmuller spaces
• Weil-Petersson metric on the universal Teichmüller space
• Plurisubharmonic features of the Teichmuller metric
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