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Доповіді НАН України. – 2007. – N 11. – С. 23–28.
Слабо плоские границы в метрических пространствах
В.И. Рязанов, Р.Р. Салимов
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 strengthening
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.
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