On the global behavior of inverse mappings in terms of prime ends
Nataliya Ilkevych, Evgeny Sevost’yanov, Sergei Skvortsov
Abstract
The paper is devoted to the study of mappings with finite distortion, actively studied recently. For mappings whose inverse satisfy the Poletsky inequality, the results on boundary behavior in terms of prime ends are obtained. In particular, it was proved that the families of the indicated mappings are equicontinuous at the points of the boundary if a certain function determining the distortion of the modulus of families of paths under the mappings is integrable.
Topics & Concepts
MathematicsPrime (order theory)Distortion (music)Boundary (topology)InverseIntegrable systemPure mathematicsFunction (biology)EquicontinuityMathematical analysisCombinatoricsComputer scienceGeometryEvolutionary biologyBiologyComputer networkBandwidth (computing)AmplifierAnalytic and geometric function theory