On the closure $\overline T$ of Teichmüller space, consider a continuous parametrization $\overline T \times \Sigma_A^+ \to \mathbb S^2$ such that Image ($t, \Sigma_A^+ = \Lambda(\Gamma_t)$). Is the Hausdorff dimension of $\Lambda(\Gamma_t)$ continuous in $t \in \overline T$?

*(Note, this problem was added by the editor to the end of Rufus' last paper [1])*

### References

- [bowen1979hausdorff] Bowen R. 1979. Hausdorff dimension of quasi-circles. Publications Mathématiques de l'IHÉS. 50:11–25.