Sur la propagation des singularités dans les variétés CR

Extension of CR-functions into weighted wedges through families of nonsmooth analytic discs

“…In particular, if V is given as in Theorem 1.4, it becomes a submanifold with boundary M at some point of A l (∂∆). The conclusion of Theorem 1.2 follows now from Theorem 1.4 (i) and the propagation of wedge extendibility along analytic discs due to Trépreau [Tr90] and Tumanov [T94]. The conclusion of Theorem 1.3 follows analogously from Theorem 1.4 (ii).…”

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

“…Trépreau's original theorem (1986) states that such an extension holds at a point p if and only if there does not exist a local complex hypersurface Σ of C n with p ∈ Σ ⊂ M . A deeper phenomenon of propagation (Trépreau, 1990) holds: if CR functions extend holomorphically to one side at a point p, a similar extension holds at every point of the CR orbit of p in M . By means of deformations of attached Bishop discs, there is an elementary (and folklore) proof that contains both the local and the global extension theorems on hypersurfaces, yielding a satisfactory understanding of the phenomenon.…”

On the Analyticity of Solutions of First-Order Nonlinear PDE

“…□ Remark 3.1. One could likewise apply Theorem 2.2 of [Trepreau, 1990] to show that the elliptic submanifolds (for the linearized vector field Lu) propagate the holomorphic extendability to wedges, as defined in [Trepreau, 1990], of the solution u. G…”