May 2, 2025
Title: h-principles for Holomorphic Partial Differential Relations in Stein Manifolds
Speaker: Guillermo Sánchez
The goal of the h-principle theory is to understand when a geometric problem is governed by the laws of differential topology. When topology (more flexible) overrides geometry (more rigid), we say that the h-principle holds in that context.
The identity principle and the resulting lack of partitions of unity endow complex geometry with great rigidity. However, there is a class of complex manifolds—Stein manifolds—in which the Oka principle, a type of h-principle for holomorphic functions, holds. The flexible properties of Stein manifolds have been exploited by F. Forstnerič and M. Slapar to establish h-principles for holomorphic immersions and submersions, and by F. Forstnerič for complex contact forms. In this talk, we will explore how these techniques can be abstracted to obtain more general h-principles in this type of complex manifolds.