Geometric regularity versus functional regularity
Germs of CR maps between real analytic hypersurfaces.
Holomorphic approximation of CR functions on tubular submanifolds of ℂ²
The purpose of this paper is to take a closer look at uniform semi-global (i.e. on compact subsets) holomorphic approximation of CR functions on tubular submanifolds in ℂ².
Holomorphic automorphisms of quadrics.
Holomorphic mappings between algebraic hypersurfaces in complex space
Holomorphic symplectic normalization of a real function
Homogeneous C R-manifolds.
Hypersurfaces Levi-plates immergées dans les surfaces complexes de courbure positive
Ideal CR submanifolds in non-flat complex space forms
An explicit representation for ideal CR submanifolds of a complex hyperbolic space has been derived in T. Sasahara (2002). We simplify and reformulate the representation in terms of certain Kähler submanifolds. In addition, we investigate the almost contact metric structure of ideal CR submanifolds in a complex hyperbolic space. Moreover, we obtain a codimension reduction theorem for ideal CR submanifolds in a complex projective space.
Infinitesimal CR automorphisms for a class of polynomial models
In this paper we study infinitesimal CR automorphisms of Levi degenerate hypersurfaces. We illustrate the recent general results of [18], [17], [15], on a class of concrete examples, polynomial models in of the form , where and are weighted homogeneous holomorphic polynomials in . We classify such models according to their Lie algebra of infinitesimal CR automorphisms. We also give the first example of a non monomial model which admits a nonlinear rigid automorphism.
Infinitesimal CR automorphisms of hypersurfaces of finite type in
We study the Chern-Moser operator for hypersurfaces of finite type in . Analysing its kernel, we derive explicit results on jet determination for the stability group, and give a description of infinitesimal CR automorphisms of such manifolds.
Intersections of totally real and holomorphic disks.
It is shown that a holomorphically embedded open disk in C2 and a totally real embedded open disk which have a common smooth boundary have nontrivial intersection.
-holomorphic discs and real analytic hypersurfaces
We give in a real analytic almost complex structure , a real analytic hypersurface and a vector in the Levi null set at of , such that there is no germ of -holomorphic disc included in with and , although the Levi form of has constant rank. Then for any hypersurface and any complex structure , we give sufficient conditions under which there exists such a germ of disc.
Levi equation and evolution of subsets of
In this Note we state some results obtained studying the evolution of compact subsets of by Levi curvature. This notion appears to be the natural extension to Complex Analysis of the notion of evolution by mean curvature.
Levi flat hypersurfaces in with prescribed boundary : stability
Levi-flat invariant sets of holomorphic symplectic mappings
We classify four families of Levi-flat sets which are defined by quadratic polynomials and invariant under certain linear holomorphic symplectic maps. The normalization of Levi- flat real analytic sets is studied through the technique of Segre varieties. The main purpose of this paper is to apply the Levi-flat sets to the study of convergence of Birkhoff's normalization for holomorphic symplectic maps. We also establish some relationships between Levi-flat invariant sets...
Lie group structures on groups of diffeomorphisms and applications to CR manifolds
We give general sufficient conditions to guarantee that a given subgroup of the group of diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group structure. These results, together with recent work concerning jet parametrization and complete systems for CR automorphisms, are then applied to determine when the global CR automorphism group of a CR manifold is a Lie group in an appropriate topology.
Liouville-type theorems for foliations with complex leaves
In this paper we discuss various problems regarding the structure of the foliation of some foliated submanifolds of , in particular Levi flat ones. As a general scheme, we suppose that is bounded along a coordinate (or a subset of coordinates), and prove that the complex leaves of its foliation are planes.
Local existence theorems with estimates for ...b on weakly pseudo convex CR manifolds.
Local holomorphic extendability and non-extendability of -functions on smooth boundaries