  It is given a canonical representation of prime ends in regular spatial
domains and, on this basis, it is studied the boundary behavior of the
so-called lower Q-homeomorphisms that are the natural generalization of the
quasiconformal mappings. In particular, it is found a series of effective
conditions on the function Q(x) for a homeomorphic extension of the given
mappings to the boundary by prime ends in domains with regular boundaries. The
developed theory is applied, in particular, to mappings of the classes of
Sobolev and Orlicz-Sobolev and also to finitely bi-Lipschitz mappings that a
far-reaching extension of the well--known classes of isometric and
quasiisometric mappings.
