Some Totally Real Embeddings of Three-Manifolds.
Special normal form of a hyperbolic CR-manifold in ℂ⁴
We give a special normal form for a non-semiquadratic hyperbolic CR-manifold M of codimension 2 in ℂ⁴, i.e., a construction of coordinates where the equation of M satisfies certain conditions. The coordinates are determined up to a linear coordinate change.
Submanifolds in the variety of planar normal sections.
Sur la propagation des singularités dans les variétés CR
Sur le prolongement holomorphe des fonctions C - R définies sur une hypersurfac réelle de classe C2 dans Cn.
Sur les remplissages holomorphes équivariants
On étudie les remplissages d’une variété CR de dimension trois par une surface complexe, sous une hypothèse d’équivariance : on suppose que beaucoup d’automorphismes CR du bord se prolongent en des biholomorphismes de tout le remplissage. On démontre dans le cas strictement pseudoconvexe un résultat d’unicité (à éclatement près).
Sur l'extension des fonctions C R
Tangential Cauchy-Riemann equations on quadratic manifolds
We study the tangential Cauchy-Riemann equations for -forms on quadratic manifolds. We discuss solvability for data in the Schwartz class and describe the range of the tangential Cauchy-Riemann operator in terms of the signatures of the scalar components of the Levi form.
The asymptotic expansion of a CR invariant and Grauert tubes.
The Euler and Pontrjagin numbers of an n-manifold in ...n.
The Euler characteristic of standard CR manifolds
In questo lavoro si calcola la caratteristica di Eulero delle varietà CR standard.
The holomorphic extension of CR functions on tube submanifolds
We show that a CR function of class , 0 ≤ k < ∞, on a tube submanifold of holomorphically extends to the convex hull of the submanifold. The extension and all its derivatives through order k are shown to have nontangential pointwise boundary values on the original tube submanifold. The -norm of the extension is shown to be no bigger than the -norm of the original CR function.
The local equivalence problem in CR geometry
This article is dedicated to the centenary of the local CR equivalence problem, formulated by Henri Poincaré in 1907. The first part gives an account of Poincaré’s heuristic counting arguments, suggesting existence of infinitely many local CR invariants. Then we sketch the beautiful completion of Poincaré’s approach to the problem in the work of Chern and Moser on Levi nondegenerate hypersurfaces. The last part is an overview of recent progress in solving the problem on Levi degenerate manifolds....
The moment-condition for the free boundary problem for functions
The Poincaré lemma and local embeddability
For pseudocomplex abstract manifolds, the validity of the Poincaré Lemma for forms implies local embeddability in . The two properties are equivalent for hypersurfaces of real dimension . As a corollary we obtain a criterion for the non validity of the Poicaré Lemma for forms for a large class of abstract manifolds of codimension larger than one.
The topology of Stein CR manifolds and the Lefschetz theorem
Necessary topological conditions are given for the closed CR embedding of a CR manifold into a Stein manifold or into a complex projective space.
Totally Real Imbeddings and the Universal Covering Spaces of Domains of Holomorphy: Some Examples.
Traces of pluriharmonic functions
Transversal Lie group actions on abstract CR manifolds.
Triviality of scalar linear type isotropy subgroup by passing to an alternative canonical form of a hypersurface
The Chern-Moser (CM) normal form of a real hypersurface in can be obtained by considering automorphisms whose derivative acts as the identity on the complex tangent space. However, the CM normal form is also invariant under a larger group (pseudo-unitary linear transformations) and it is this property that makes the CM normal form special. Without this additional restriction, various types of normal forms occur. One of them helps to give a simple proof of a (previously complicated) theorem about...