New Applications of Symplectic Topology in Several Complex Variables

Abstract

This is a survey of complex analytic implications of recent development in symplectic topology. Keywords Stein manifolds • Weinstein manifolds • Polynomial convexity • Rational convexityThe interplay between symplectic geometry and complex analysis was explored in our book [10] and since then was further developed, e.g., in [13,42]. Meanwhile, the symplectic side of the story was greatly developed. This, in turn, yields new consequences for complex analysis which we discuss in this survey.To the memory of Gennadi Henkin Y. Eliashberg is partially supported by the NSF Grant DMS-1807270.