Gregor Herbort

The Bergman metric on hyperconvex domains

Abstract. In this article it is shown that the Bergman metric on a bounded hyperconvex domain in

Pseudoconvex domains of semiregular type

\mathbb{C}^n

On the invariant differential metrics near pseudoconvex boundary points where the Levi form has corank one

is always complete. A counterexample demonstrates, that the converse conclusion fails in general.

Geometric and analytic boundary invariants on pseudoconvex domains. Comparison results

In this article we develop the geometric tools needed for obtaining more precise analytic information than known so-far on a relatively large class of bounded pseudoconvex domains Ω ⊂ ℂ n with C ∞-smooth boundary of finite type.

THE PLURICOMPLEX GREEN FUNCTION ON PSEUDOCONVEX DOMAINS WITH A SMOOTH BOUNDARY

Let D be a bounded domain in C n ; in the space L 2 (D) of functions on D which are square-integrable with respect to the Lebesgue measure d 2n z the holomorphic functions form a closed subspace H 2 (D) . Therefore there exists a well-defined orthogonal projection P D : L 2 (D) → H 2 (D) with an integral kernel K D :D × D → C, the Bergman kernel function of D . An explicit computation of this function directly from the definition is possible only in very few cases, as for instance the unit ball, the complex “ellipsoids” , or the annulus in the plane. Also, there is no hope of getting information about the function K D in the interior of a general domain. Therefore the question for an asymptotic formula for the Bergman kernel near the boundary of D arises.

On the Dimension of the Bergman Space for Some Unbounded Domains

AbstractWe consider for smooth pseudoconvex bounded domains Ω ⊂ ℂn of finite type as local analytic invariants on the boundary the growth orders of the Bergman kernel and the Bergman metric and the best possible order of subellipticity ε1 > 0 for the

Weights of holomorphic extension and restriction

\bar \partial - Neumann

On the Bergman metric on bounded pseudoconvex domains an approach without the Neumann operator

problem. Furthermore, we consider as local geometric invariants on ∂Ω the order of extendability, the exponent of extendability, the 1-type, and the multitype. Various new inequalities between these invariants are proved, giving in particular analytic information from geometric input. On the other hand, a careful consideration of several series of examples of such domains Ω shows that starting fromn ≥ 3 (essentially) each of these invariants is independent of the remaining ones.