University of Ljubljana
Area(s) of Expertise
Complex Analysis, Several Complex Variables
Josip Globevnik works in complex analysis, in particular in the theory of functions of several complex variables. In his work he has studied the values of vector valued holomorphic functions, boundary values of holomorphic functions of several variables and analytic sets, holomorphic embeddings of domains in the complex plane, integral characterization of holomorphic functions of one variable, integral characterization of boundary values of holomorphic functions of several variables, analytic discs with boundaries in maximally real submanifolds and characterization of boundary values of holomorphic functions in terms of the argument principle. Berit Stensones and Josip Globevnik proved in 1995 that every bounded, finitely connected domain in C without isolated points in the boundary can be properly holomorphically embedded to C^2. In 2000 Globevnik proved that every point in a Stein manifold M is contained in the image of a proper holomorphic map from the unit disc to M. In 2015 he constructed a complete complex hypersurface in the unit ball in C^N and thus obtained a complete solution of a problem of P. Yang from 1977. This work is being continued together with A.Alarcon and F.J.Lopez – in particular, it has been proved that there is a complete, proper holomorphic embedding from the disc to the ball in C^2.