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Equicontinuity of homeomorphisms with unbounded characteristic

Abstract

The article is devoted to the study of the boundary properties of homeomorphisms f: DD′, D,D′ ⊂ ℝn, 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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Correspondence to E. A. Sevostyanov.

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Original Russian Text © E. A. Sevostyanov, 2012, published in Matematicheskie Trudy, 2012, Vol. 15, No. 1, pp. 178–204.

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Sevostyanov, E.A. Equicontinuity of homeomorphisms with unbounded characteristic. Sib. Adv. Math. 23, 106–122 (2013). https://doi.org/10.3103/S1055134413020053

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Keywords

  • modulus of a family of curves
  • open discrete mapping
  • capacity of a condenser
  • boundary behavior of a mapping
  • QED-domain