Mathematics – Complex Variables
Scientific paper
2007-01-19
International Mathematics Research Surveys Volume 2006 (2006) (12/2006) 287 pages
Mathematics
Complex Variables
283 pages ; 33 illustrations ; 16 open problems http://www.hindawi.com/journals/imrs/
Scientific paper
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.
Merker Joel
Porten Egmont
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