Propagation of holomorphic extendability of CR functions

Hanges, Nicholas; Trèves, François

doi:10.1007/bf01456878

Cited by 50 publications

(33 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By the Hanges-Treves propagation theorem (see [HT83]), it suffices to show that f extends holomorphically to a full neighborhood of some particular point p 1 ∈ E ⊂ M. We shall first choose a point p 0 ∈ E so that Theorem 2.1 is applicable. First, since M is of 1-infinite type along E, M is in fact of 1-infinite type 2 outside a proper real-analytic variety of E in view of Proposition 3.1.…”

mentioning

confidence: 99%

On the analyticity of CR mappings between nonminimal hypersurfaces

Ebenfelt¹

2002

Mathematische Annalen

View full text Add to dashboard Cite

Abstract. Let M ⊂ C 2 be a connected real-analytic hypersurface containing a connected complex hypersurface E ⊂ C 2 , and let f : M → C 2 be a smooth CR mapping sending M into another real-analytic hypersurface M ′ ⊂ C 2 . In this paper, we prove that if f does not collapse E to a point and does not collapse M into the image of E, and if the Levi form of M vanishes to first order along E, then f is real-analytic in a neighborhood of E. In general, the corresponding statement is false if the Levi form of M vanishes to second order or higher, in view of an example due to the author. We also show analogous results in higher dimensions provided that the target M ′ satisfies a certain nondegeneracy condition.The main ingredient in the proof, which seems to be of independent interest, is the prolongation of the system defining a CR mapping sending M into M ′ to a Pfaffian system on M with singularities along E. The nature of the singularity is described by the order of vanishing of the Levi form along E.

show abstract

mentioning

confidence: 99%

On the analyticity of CR mappings between nonminimal hypersurfaces

Ebenfelt¹

2002

Mathematische Annalen

View full text Add to dashboard Cite

show abstract

“…(See [14,Chapter 1.7]). The main result in this direction is due to Hanges and Trèves [8], and was proved using microlocal techniques. See the papers [2] and [11] for other instances of this phenomenon.…”

Section: Introduction and Main Resultsmentioning

confidence: 91%

An extension theorem for regular functions of two quaternionic variables

Baracco

Fassina

Pinton

2020

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…(c) We now use the theory of propagation of wedge extendibility along discs for each CR function F | M by [12] which develops [8]. We put a suffix s in the notation of the disc ∆ s to specify its radius, and define (3.11) for all stationary discs φ tangent to ∂D 2 at τ =0.…”

Section: The Main Resultsmentioning

confidence: 99%