On the boundary value problem for harmonic maps of the Poincaré disc

DOI10.1007/BF02882940zbMath0905.30017MaRDI QIDQ1387479

Zhong Li

Publication date: 2 February 1999

Published in: Chinese Science Bulletin (Search for Journal in Brave)

zbMATH Keywords

quadratic differentialsPoincaré metricquasiconformal extensionHopf differentialquasisymmetric homeomorphismscomplex dilation

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Teichmüller theory for Riemann surfaces (30F60) Quasiconformal mappings in the complex plane (30C62)

Related Items (9)

$\overline {\partial }$-energy integral and harmonic mappings ⋮ Convergence of harmonic maps on the Poincaré disk ⋮ Harmonic Teichmüller mappings ⋮ The inverse of a \(\sigma (z)\)-harmonic diffeomorphism ⋮ The cross-ratio distortion of integrably asymptotic affine homeomorphism of unit circle ⋮ Harmonicity of the inverse of a harmonic diffeomorphism ⋮ A note on harmonic quasiconformal mappings ⋮ Harmonic extensions of symmetric maps ⋮ Finite distortion functions and Douglas-Dirichlet functionals

Cites Work

• The boundary correspondence under quasiconformal mappings
• On the Gerstenhaber-Rauch principle
• The Teichmüller theory of harmonic maps
• Constant mean curvature surface, harmonic maps, and universal Teichmüller space
• On univalent harmonic maps between surfaces
• The heat equation and harmonic maps of complete manifolds
• Gauss maps of spacelike constant mean curvature hypersurfaces of Minkowski space
• On Homotopic Harmonic Maps
• On Quasiconformal Mappings which Keep the Boundary Points Fixed
• Harmonic Mappings of Riemannian Manifolds
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