Слабо плоские границы в метрических пространствах

Abstract

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.