On Equicontinuous Families of Mappings of Metric Spaces

Abstract

We obtain analogs of the results on equicontinuity of families of quasiregular mappings that take no values from a fixed continuum. We prove that these families are equicontinuous whenever the quasiconformality characteristics of the mappings have finite mean oscillation at every inner point. In this context, we also prove the equicontinuity of generalized quasiisometries of Riemannian manifolds.