Problem 157

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