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Enveloppes polynomiales de variétés réelles dans C2.

Boris Gourlay (1993)

Publicacions Matemàtiques

We present here three examples concerning polynomial hulls of some manifolds in C2.1. Some real surfaces with equation w = P (z,z') + G(z) where P is a homogeneous polynomial of degree n and G(z) = o(|z|n) at 0 which are locally polynomially convex at 0.2. Some real surfaces MF with equation w = zn+kz'n + F(z,z') such that the hull of Mf ∩ B'(0,1) contains a neighbourhood of 0.3. A contable union of totally real planes (Pj) such that B'(0,1) ∩ (∪j∈N Pj) is polynomially convex.

Extending Tamm's theorem

Lou van den Dries, Chris Miller (1994)

Annales de l'institut Fourier

We extend a result of M. Tamm as follows:Let f : A , A m + n , be definable in the ordered field of real numbers augmented by all real analytic functions on compact boxes and all power functions x x r : ( 0 , ) , r . Then there exists N such that for all ( a , b ) A , if y f ( a , y ) is C N in a neighborhood of b , then y f ( a , y ) is real analytic in a neighborhood of b .

Extension of CR functions to «wedge type» domains

Andrea D'Agnolo, Piero D'Ancona, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let X be a complex manifold, S a generic submanifold of X R , the real underlying manifold to X . Let Ω be an open subset of S with Ω analytic, Y a complexification of S . We first recall the notion of Ω -tuboid of X and of Y and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for ¯ b to the extendability of C R functions on Ω to Ω -tuboids of X . Next, if X has complex dimension 2, we give results on extension...

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