# On boundary behavior of mappings on Riemannian manifolds in terms of prime ends

## TL;DR

This paper investigates the boundary behavior of generalized ring mappings on Riemannian manifolds, establishing conditions for continuous extension and equicontinuity using prime ends, thus extending classical quasiconformal mapping theory.

## Contribution

It introduces new theorems on boundary extension and equicontinuity for ring mappings on Riemannian manifolds using prime ends, generalizing previous quasiconformal results.

## Key findings

- Theorems on continuous boundary extension of ring mappings.
- Results on equicontinuity of these mappings in domain closures.
- Extension of classical quasiconformal boundary behavior to Riemannian manifolds.

## Abstract

A boundary behavior of ring mappings on Riemannian manifolds, which are generalization of quasiconformal mappings by Gehring, is investigated. In terms of prime ends, there are obtained theorems about continuous extension to a boundary of classes mentioned above. In the terms mentioned above, there are obtained results about equicontinuity of these classes in the closure of the domain.