Families of strictly pseudoconvex domains and peak functions

We prove that given a family $(G_t)$ of strictly pseudoconvex domains varying in $\mathcal{C}^2$ topology on domains, there exists a continuously varying family of peak functions $h_{t,\zeta}$ for all $G_t$ at every $\zeta\in\partial G_t.

Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems