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Article Dans Une Revue International Mathematics Research Surveys Année : 2006

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

Résumé

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.
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Dates et versions

hal-00125098 , version 1 (19-01-2007)

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Joël Merker, Egmont Porten. Holomorphic extension of CR functions, envelopes of holomorphy and removable singularities. International Mathematics Research Surveys, 2006, Volume 2006 (2006), 287 p. ⟨hal-00125098⟩
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