On extension of some generalizations of quasiconformal mappings to a boundary
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This work is devoted to the investigation of ring Q-homeomorphisms. We formulate conditions for a function Q(x) and the boundary of a domain under which every ring Q-homeomorphism admits a homeomorphic extension to the boundary. For an arbitrary ring Q-homeomorphism f: D → D’ with Q ∈ L 1(D); we study the problem of the extension of inverse mappings to the boundary. It is proved that an isolated singularity is removable for ring Q-homeomorphisms if Q has finite mean oscillation at a point.
KeywordsNeighborhood Versus QUASICONFORMAL Mapping Continuous Extension Beltrami Equation Arbitrary Ring
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