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LOCALLY UNIFORM DOMAINS AND QUASICONFORMAL MAPPINGS

We document various properties of the classes of locally uniform and weakly linearly locally connected domains. We describe the boundary behavior for quasiconformal homeomorphisms of these domains and exhibit certain metric conditions satisfied by such maps. We characterize the quasiconformal homeomorphisms from locally uniform domains onto uniform domains. We furnish conditions which ensure that a homeomorphism maps locally uniform domains to locally uniform domains. Everywhere examples are provided which illustrate the sharpness of our results.