Horospheres in degenerate 3-manifolds

TL;DR

This paper investigates the properties of horospheres in hyperbolic 3-manifolds with degenerate ends, focusing on the behavior of almost minimizing geodesics in thin regions.

Contribution

It provides new insights into the structure of horospheres and geodesics in degenerate hyperbolic 3-manifolds, a less explored area in geometric topology.

Findings

Characterization of horospheres in degenerate 3-manifolds

Analysis of almost minimizing geodesics passing through thin parts

Connections between end degeneracy and geodesic behavior

Abstract

We study horospheres in hyperbolic 3-manifolds $M$ all whose ends are degenerate. Towards this, we study which almost minimizing geodesics in $M$ go through arbitrarily thin parts.