# Exotic limit sets of Teichm\"uller geodesics in the HHS boundary

## TL;DR

This paper demonstrates that Teichmüller geodesic rays can have highly non-unique limit sets in the HHS boundary, showing the boundary's complex and flexible structure.

## Contribution

It proves that Teichmüller geodesic rays can have arbitrary limit sets in the HHS boundary, answering a question about boundary convergence.

## Key findings

- Teichmüller geodesic rays do not necessarily converge to a unique boundary point.
- The limit set of a geodesic ray can be almost any topologically allowed subset.
- The result highlights the complexity of the HHS boundary for Teichmüller space.

## Abstract

We answer a question of Durham, Hagen, and Sisto, proving that a Teichm\"uller geodesic ray does not necessarily converge to a unique point in the hierarchically hyperbolic space boundary of Teichm\"uller space. In fact, we prove that the limit set can be almost anything allowed by the topology.