ICM 2026 Invited Section Lecture – Franc Forstneric

From Stein Manifolds to Oka Manifolds: The H-Principle in Complex Analysis In this talk, I will describe the main developments in the theory of the h-principle in complex analysis and geometry, better known as the Oka principle. I will present the key notions of Oka manifolds and Oka maps, which developed from the Oka-Grauert principle and Gromov's theory of elliptic complex manifolds and elliptic holomorphic submersions, and their characterization by simpler approximation and ellipticity conditions. I will discuss recent and ongoing developments, open problems, and mention applications to the classical theory of minimal surfaces. Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices