Alexandre Sukhov

ON BOUNDARY RIGIDITY AND REGULARITY OF HOLOMORPHIC MAPPINGS

We prove that a continuous CR mapping between two pseudoconvex hypersurfaces of finite type in

Analyticité des applications Cℛ

{\mathbb C}^2

PROPER J-HOLOMORPHIC DISCS IN STEIN DOMAINS OF DIMENSION 2

is smooth if at least one of the hypersurfaces is strictly pseudoconex.

Regularity of CR maps between convex hypersurfaces of finite type

We establish sufficient conditions for the analyticity of a smooth CR mapping between two real analytic manifolds.

EXTENSION OF CR MAPS OF POSITIVE CODIMENSION

We prove the existence of global Bishop discs in a strictly pseudoconvex Stein domain in an almost complex manifold of complex dimension 2.

Gromov's Non-Squeezing Theorem and Beltrami Type Equation

We study rigidity and regularity properties of CR maps between smooth convex hypersurfaces of finite type in Cn+1.

Rational approximation and Lagrangian inclusions

We study the holomorphic extendability of smooth CR maps between real analytic strictly pseudoconvex hypersurfaces in complex affine spaces of different dimensions.

On maps of CR manifolds and transformations of differential equations

We introduce a method for constructing J-complex discs. The method only uses the standard scheme for solving the Beltrami equation and the Schauder principle. As an application, we give a short self-contained proof of Gromovs Non-Squeezing Theorem.

Dicritical singularities and laminar currents on Levi-flat hypersurfaces

We show that a Lagrangian inclusion in

REGULARIZED MAXIMUM OF STRICTLY PLURISUBHARMONIC FUNCTIONS ON AN ALMOST COMPLEX MANIFOLD

\mathbb C^2