On the boundary behavior of mappings in the class \(W^{1,1}_{\mathrm{loc}}\) on Riemann surfaces

DOI10.1007/s11785-016-0618-4zbMath1379.30029OpenAlexW2334104700MaRDI QIDQ1683595

Peng Zhang

Publication date: 1 December 2017

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-016-0618-4

zbMATH Keywords

Riemann surfacesmappings of finite distortioncontinuous boundary values

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Boundary value problems in the complex plane (30E25) Riemann surfaces (30F99)

Related Items (15)

On the local and boundary behaviour of mappings of factor spaces ⋮ Local behavior of mappings of metric spaces with branching ⋮ Prime ends in the mapping theory on the Riemann surfaces ⋮ Boundary behaviour of open, light mappings in metric measure spaces ⋮ On the radial limits of mappings on Riemannian manifolds ⋮ On the boundary extension of mappings on Riemannian surfaces in terms of prime ends ⋮ Mappings with finite length distortion and prime ends on Riemann surfaces ⋮ On a Poletskii-type inequality for mappings of the Riemannian surfaces ⋮ On boundary extension of mappings in metric spaces in the terms of prime ends ⋮ On equicontinuous families of mappings of metric spaces ⋮ On the local behavior of Sobolev classes on two-dimensional Riemannian manifolds ⋮ On equicontinuity of families of mappings between Riemannian surfaces with respect to prime ends ⋮ Cluster sets theorems on metric measure spaces ⋮ On Poleckii-type modular inequalities ⋮ О классах Орлича — Соболева на фактор-пространствах

Cites Work

• On integral conditions in the mapping theory
• The Beltrami equation. A geometric approach
• Extremal length and functional completion
• Surfaces and planar discontinuous groups. Revised and expanded transl. from the German by J. Stillwell
• On the theory of \(Q(x)\)-homeomorphisms.
• On mappings in the Orlicz--Sobolev classes on Riemannian manifolds
• On boundary behavior of generalized quasi-isometries
• Boundary behavior and the Dirichlet problem for Beltrami equations
• Boundary behavior of ring Q-homeomorphisms in metric spaces
• Moduli in Modern Mapping Theory
• On Mappings with Integrable Dilatation
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