On a construction of the normal Cartan connections for CR-structures
On boundary Hilbert differential complexes
On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle
In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Levi-flat “hat”. In our main theorem, we show that every -smooth CR diffeomorphism between two globally minimal real analytic hypersurfaces in () is real analytic at every point...
On local geometry of finite multitype hypersurfaces
This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in . We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite constructive algorithm for computing multitype is described. Analogous results for decoupled hypersurfaces are given.
On some rigidity properties of mappings between CR-submanifolds in complex space
We survey some recent results on holomorphic or formal mappings sending real submanifolds in complex space into each other. More specifically, the approximation and convergence properties of formal CR-mappings between real-analytic CR-submanifolds will be discussed, as well as the corresponding questions in the category of real-algebraic CR-submanifolds.
On Strict Levi q-Convexity and q-Concavity on Domains with Piecewise Smooth Boundaries.
On the convergence of normalizations of real analytic surfaces near hyperbolic complex tangents.
On the Curvature of CR-Structures and its Covariant Derivatives.
On the extension of C.R. functions.
On the extension of holomorphic functions across a real hypersurface.
On the hull of holomorphy of an -manifold in
On the local solution of the tangential Cauchy-Riemann equations
On the Nature of Thin Complements of Complete Kähler Metrics.
On the partial algebraicity of holomorphic mappings between two real algebraic sets
The rigidity properties of the local invariants of real algebraic Cauchy-Riemann structures imposes upon holomorphic mappings some global rational properties (Poincaré 1907) or more generally algebraic ones (Webster 1977). Our principal goal will be to unify the classical or recent results in the subject, building on a study of the transcendence degree, to discuss also the usual assumption of minimality in the sense of Tumanov, in arbitrary dimension, without rank assumption and for holomorphic...
On the Polynomial Convexity of the Union ot Two Maximal Totally Real Subspaces of Cn.
On the proof of Kuranishi's embedding theorem
On the real analytic Levi flat hypersurfaces in complex tori of dimension two
We compute the Levi form of the logarithm of the distance function for real hypersurfaces in two dimensional complex tori, and discuss the characterization of Levi flat hypersurfaces there.
On the smoothness of Levi-foliations.
We study the regularity of the induced foliation of a Levi-flat hypersurface in Cn, showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question.
On the space of the analytic discs which are transversal to a smooth real hypersurface of
On totally real submanifolds in a nearly Kähler manifold.