# Schwarz lemma for harmonic mappings between Riemann surfaces

## TL;DR

This paper establishes a Schwarz type lemma for harmonic mappings between the unit disk and a geodesic line in a Riemann surface, extending classical results to a broader geometric context.

## Contribution

It introduces a Schwarz lemma specifically for harmonic mappings between the unit disk and geodesic lines in Riemann surfaces, a novel extension of classical complex analysis results.

## Key findings

- Proves a Schwarz lemma for harmonic mappings in Riemann surfaces.
- Extends classical Schwarz lemma to harmonic maps between specific geometric structures.
- Provides new bounds or conditions for harmonic mappings in this setting.

## Abstract

We prove a Schwarz type lemma for harmonic mappings between the unit and a geodesic line in a Riemenn surface.