On locally quasiconformal mappings.

A homeomorphism w = f( z) of a domain D is called a locally quasiconformal mapping, if for each subdomain D′ of D with $$\overline {D'} \subset D$$, the restriction of f( z) on D′ is a quasiconformal mapping. We give some conditions for a measurable function µ( z) on the unit disc to be the complex dilatation of a locally quasiconformal mapping f which can be homeomorphically extended to the closed unit disc. [ABSTRACT FROM AUTHOR]