Rasul Shafikov

Boundary regularity of correspondences in ℂn

AbstractLetM, M′ be smooth, real analytic hypersurfaces of finite type in ℂn and

Rational approximation and Lagrangian inclusions

\hat f

Discs in hulls of real immersions into Stein manifolds

a holomorphic correspondence (not necessarily proper) that is defined on one side ofM, extends continuously up toM and mapsM to M′. It is shown that

Distributional boundary values of holomorphic functions on product domains

\hat f

Extension of holomorphic maps between real hypersurfaces of different dimension

must extend acrossM as a locally proper holomorphic correspondence. This is a version for correspondences of the Diederich-Pinchuk extension result for CR maps.

POLYNOMIALLY CONVEX HULLS OF SINGULAR REAL MANIFOLDS

Given a real analytic (or, more generally, semianalytic) set R in Cn (viewed as R2n), there is, for every p ∈ R, a unique smallest complex analytic germ Xp that contains the germ Rp. We call dimC Xp the holomorphic closure dimension of R at p. We show that the holomorphic closure dimension of an irreducible R is constant on the complement of a closed proper analytic subset of R, and we discuss the relationship between this dimension and the CR dimension of R.