Moebius structures, hyperbolic ends and $k$-surfaces in hyperbolic space

TL;DR

This paper introduces M"obius structures and hyperbolic ends, exploring their applications to the theory of $k$-surfaces in 3D hyperbolic space, providing foundational insights into their geometric relationships.

Contribution

It offers a foundational introduction to M"obius structures and hyperbolic ends, linking them to the study of $k$-surfaces in hyperbolic space, which is a novel integration.

Findings

Established basic connections between M"obius structures and hyperbolic ends.

Applied these concepts to analyze properties of $k$-surfaces.

Provided new perspectives on the geometry of hyperbolic 3-manifolds.

Abstract

We present a basic introduction to the theories of M\"obius structures and hyperbolic ends and we study their applications to the theory of $k$-surfaces in $3$-dimensional hyperbolic space.