On equicontinuous families of mappings in metric spaces

Evgeniy Petrov; Evgeny Sevost'yanov; Sergei Skvortsov

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On equicontinuous families of mappings in metric spaces

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arxiv 1707.05886 v3 pith:N7C65N5L submitted 2017-07-18 math.CV

Evgeny Sevost'yanov , Sergei Skvortsov , Evgeniy Petrov This is my paper

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keywords mappingsfamiliesequicontinuityequicontinuousfinitemetricobtainedspaces

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The article is devoted to the study of mappings with finite distortion in metric spaces. Analogues of results relating to equicontinuity and normality of families of quasiregular mappings are obtained. It is proved that the indicated families are equicontinuous if the characteristic of the mappings has a finite mean oscillation at each inner point, and the maps omit a certain fixed continuum. An equicontinuity of generalized quasiisometries on Riemannian manifolds is also obtained.

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