On boundary and global behavior of mappings with branching on Riemannian surfaces

TL;DR

This paper studies the boundary and global behavior of non-homeomorphic Sobolev class mappings on Riemannian surfaces, providing estimates on distortion and boundary behavior insights.

Contribution

It introduces new distortion estimates and boundary behavior results for Sobolev mappings between Riemannian surfaces, extending understanding of their global properties.

Findings

Derived estimates for distortion of moduli of curve families

Established boundary behavior results for Sobolev mappings

Analyzed global behavior of non-homeomorphic mappings on Riemannian surfaces

Abstract

In the present paper, we investigate non-homeomorphic mappings of Riemannian surfaces of Sobolev class. We have obtained some estimates of distortion of moduli of families of curves. As consequence, we have obtained results about the boundary behavior of such mappings between domains on Riemannian surfaces.