Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of $0$ in ${ℂ}^p$, for some $p\>0$) or differentiable (parametrized by an open neighborhood of $0$ in ${ℝ}^p$, for some $p\>0$) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point $t$ of the parameter space, the fiber over $t$ of the first family is biholomorphic to the fiber over $t$ of the second family. Then, under which conditions are the...

Si illustrano alcuni sviluppi della teoria delle foliazioni di Monge-Ampère e delle sue applicazioni alla classificazione delle varietà complesse non compatte.