Holomorphic extension of CR functions, envelopes of holomorphy and removable singularities

Abstract

This is an extensive (published) survey on CR geometry, whose major themes are: formal analytic reflection principle; generic properties of Systems of (CR) vector fields; pairs of foliations and conjugate reflection identities; Sussmann's orbit theorem; local and global aspects of holomorphic extension of CR functions; Tumanov's solution of Bishop's equation in Hoelder classes with optimal loss of smoothness; wedge-extendability on C^2,a generic submanifolds of C^n consisting of a single CR orbit; propagation of CR extendability and edge-of-the-wedge theorem; Painlevé problem; metrically thin singularities of CR functions; geometrically removable singularities for solutions of the induced d-barre. Selected theorems are fully proved, while surveyed results are put in the right place in the architecture.