Prime Ends in Theory of Mappings with Finite Distortion in the Plane

Abstract

In the present paper, it was studied the
boundary behavior of the so-called lower Q-homeomorphisms in the
plane that are a natural generalization of the quasiconformal
mappings. In particular, it was found a series of effective
conditions on the function Q(z) for a homeomorphic extension of
the given mappings to the boundary by prime ends. The
developed theory is applied to mappings with finite distortion
by Iwaniec, also to solutions of the Beltrami equations, as well as
to finitely bi--Lipschitz mappings that a far-reaching extension of
the known classes of isometric and quasiisometric mappings.