Quasiconformally Instable Disc Bundles with Complex Structures

We discuss deformations and the quasiconformal instability of the Kähler geometry of disc bundles that are locally modeled on symmetric rank-one manifolds. The Kähler geometry of these manifolds is associated with natural complex or hypercomplex structures of pinched negative sectional curvature and infinite volume. Their fundamental groups are isomorphic to discrete subgroups of $\mathrm {PU}(n,1)$, $\mathrm {PSp}(n,1)$, or $\mathrm F_4^{-20}$.