On equicontinuity of families of mappings between Riemannian surfaces with respect to prime ends
Abstract
Given a domain of some Riemannian surface,
we consider questions related to the possibility of a continuous
extension to the boundary of one class of Sobolev mappings. It is
proved that such maps have a continuous boundary extension in terms
of prime ends, and under some additional restrictions their families
are equicontinuous at inner and boundary points of the domain. We
have separately considered the cases of homeomorphisms and mappings
with branching.
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