Main themes of Forstnerič’s research work include proper holomorphic mappings and embeddings, Cauchy-Riemann geometry, holomorphic convexity, holomorphic automorphism and their applications, the Oka-Grauert-Gromov principle, elliptic complex geometry, embeddings and directed immersions of Riemann surfaces, and applications of complex analysis to the theory minimal surfaces.
In the period since 2000, the main topic of his research has been modern Oka theory and its applications. Forstnerič began by clarifying the seminal work of M. Gromov in a series of joint papers with J. Prezelj around 2000.
In 2005 he found a simple necessary and sufficient condition on a complex manifold to satisfy the basic Oka principle. In 2009 Forstnerič proved that this condition also implies the parametric Oka principle and showed that all main Oka type conditions are pairwise equivalent. At that point he introduced in the literature the class of Oka manifolds. This is the main topic of his monograph Stein Manifolds and Holomorphic Mappings published by Springer-Verlag in 2011.
In recent years Forstnerič collaborated with A. Alarcon and F. J. Lopez from University of Granada in applications of modern Oka theory in the theory of minimal surfaces in Euclidean spaces.