Edda Sigurdardottir: Tame families of Stein manifolds

Abstract: We study families of manifolds with a fixed smooth structure but continuously varying complex structures, and ask when classical results in complex analysis hold uniformly across the family. We introduce a notion of tameness and show several equivalent ways to define it. We prove that tameness characterizes when the Oka–Weil approximation theorem behaves continuously with the parameter, as well as global solutions to the Cauchy–Riemann problem. This is joint work with Franc Forstnerič.