Слабо плоские границы в метрических пространствах - Рязанов, В.И.; Салимов, Р.Р. (Видавничий дім "Академперіодика" НАН України, 2007)
It has been shown that the domains with the so-called weakly ﬂat boundaries are locally pathwise
connected at the boundary points. On this base, the far-reaching generalization and strengtheni-
ng of the well-known Gehring–Martio theorem (1985) on a homeomorphic extension to the
boundary of quasiconformal mappings between quasiextremal distance domains in Rn, n > 2,
are obtained. The domains with weakly ﬂat boundaries form a new widest type of domains, vast
classes of topological mappings between which admit a homeomorphic extension to the boundary.