  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.
