Abstract
The article is devoted to the study of the boundary properties of homeomorphisms f: D → D′, D,D′ ⊂ ℝ n , satisfying some geometric conditions responsible for the control of the measure of distortion of families of curves in D. Under additional requirements on the boundaries ∂D and ∂D′ of the domains, we prove that the family of all such homeomorphisms is equicontinuous in \(\bar D\).
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