On equicontinuous families of mappings in metric spaces

2017/07/18 by Evgeny Sevost’yanov, Sevost'yanov, Evgeny, Sergei Skvortsov +3
Mathematics · #30C65 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1707.05886

openalex publication_date 2017/07/18 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

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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