Sergey Pinchuk

Domains in C n+1 with noncompact automorphism group

AbstractWe consider certain pseudoconvex domains in Cn+1 and show that if the automorphism group is noncompact, then the domain is equivalent to

Analytic sets extending the graphs of holomorphic mappings

E_m = \{ |w|^2 + |z_1 |^{2m} + |z_2 |^2 + \cdots + |z_n |^2< 1\}

THE INVERSE OF A CR-HOMEOMORPHISM IS CR

for some integerm ≥ 1.

EXTENSION OF CR MAPS OF POSITIVE CODIMENSION

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

The geometric reflection principle in several complex variables: a survey

{\mathbb C}^2

Upper semi-continuity of the Kobayashi-Royden pseudo-norm, a counterexample for Hölderian almost complex structures

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

Dicritical singularities and laminar currents on Levi-flat hypersurfaces

Let D, D′ ⊂ ℂn be bounded domains with smooth real analytic boundaries and ƒ: D → D′ be a proper holomorphic map. Our main result implies that if the graph of ƒ extends as an analytic set to a neighborhood of a poìnt (a, a′) ∈ ∂D × 3D′ with a′ ∈ clƒ(a), then ƒ extends holomorphically to a neighborhood of a.

Дикритические особенности и ламинарные потоки на Леви-плоских гиперповерхностях@@@Dicritical singularities and laminar currents on Levi-flat hypersurfaces

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