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; Painlev\'{e} 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.
Keywords
Cite
@article{arxiv.math/0701531,
title = {Holomorphic extension of CR functions, envelopes of holomorphy and removable singularities},
author = {Joël Merker and Egmont Porten},
journal= {arXiv preprint arXiv:math/0701531},
year = {2007}
}
Comments
283 pages ; 33 illustrations ; 16 open problems http://www.hindawi.com/journals/imrs/