Alberto Saracco

HYPERBOLICITY IN UNBOUNDED CONVEX DOMAINS

Abstract We provide several equivalent characterizations of Kobayashi hyperbolicity in unbounded convex domains in terms of peak and anti-peak functions at infinity, affine lines, Bergman metric and iteration theory.

NON COMPACT BOUNDARIES OF COMPLEX ANALYTIC VARIETIES

We treat the boundary problem for complex varieties with isolated singularities, of dimension greater than one, which are contained in a certain class of strongly pseudoconvex, not necessarily bounded open subsets of ℂn. We deal with the problem by cutting with a family of complex hyperplanes and applying the classical Harvey–Lawsons theorem for the bounded case [6].

Carleson measures for Hardy and Bergman spaces in the quaternionic unit ball

We study a characterization of slice Carleson measures and of Carleson measures for the both the Hardy spaces

Semiglobal extension of maximally complex submanifolds

H^p(\mathbb B)

Cohomology and removable subsets

and the Bergman spaces

Non compact boundaries of complex analytic varieties in Hilbert spaces

\mathcal A^p(\mathbb B)

On deformations of compact balanced manifolds

of the quaternionic unit ball

CONVEXITY PROPERTIES AND COMPLETE HYPERBOLICITY OF LEMPERT'S ELLIPTIC TUBES

\mathbb B

Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains

. In the case of Bergman spaces, the characterization is done in terms of the axially symmetric completion of a pseudohyperbolic disc in a complex plane. We also show that a characterization in terms of pseudohyperbolic balls is not possible.

Toeplitz operators and Carleson measures in strongly pseudoconvex domains

Let A be a domain of the boundary of a (weakly) pseudoconvex domain O of C^n and M a smooth, closed, maximally complex submanifold of A We find a subdomain E of \C^n, depending only on O and A, and a complex variety W contained in E such that bW = M. Moreover, a generalization to analytic sets of depth at least 4 is given. doi:10.1017/S0004972711002498