Peter Pflug

Extension of holomorphic functions

Riemann domains - Riemann domains over Cn holomorphic functions examples of Riemann regions holomorphic extension of Riemann domains the boundary of a Riemann domain union, intersection, and direct limit of Riemann domains domains of existence maximal holomorphic extensions liftings of holomorphic mappings I holomorphic convexity Riemann surfaces pseudocenvexity - Plurisubharmonic functions pseudoconvexity the Kiselman minimum principle d-operator solution of the Levi problem regular solutions approximation the Remmert embedding theorem the Docquier-Grauert criteria the division theorem spectrum liftings of holomorphic mappings II envelopes of holomorphy for special domains - Univalent envelopes of holomorphy k-tubular domains matrix Reinhardt domains the envelope of holomorphy of X/M separately holomorphic functions extension of meromorphic functions existence domains of special families of holomorphic functions - special domains the Ohsawa-Takegoshi extension theorem the Skoda division theorem the Catlin-Hakim-Sibony theorem structure of envelopes of holomorphy.

The Lempert function of the symmetrized polydisc in higher dimensions is not a distance

We prove that the Lempert function of the symmetrized polydisc in dimension greater than two is not a distance.

DESCRIPTION OF ALL COMPLEX GEODESICS IN THE SYMMETRIZED BIDISC

In the paper we find effective formulas for the complex geodesics in the symmetrized bidisc.

Exhausting domains of the symmetrized bidisc

We show that the symmetrized bidisc may be exhausted by strongly linearly convex domains. It shows in particular the existence of a strongly linearly convex domain that cannot be exhausted by domains biholomorphic to convex ones.

A general cross theorem with singularities

We present a general cross theorem for separately holomorphic and meromorphic functions with singularities.

Behavior of the Bergman kernel and metric near convex boundary points

The boundary behavior of the Bergman metric near a convex boundary point z 0 of a pseudoconvex domain D C C is studied. It turns out that the Bergman metric at points z ∈ D in the direction of a fixed vector X 0 E C n tends to infinity, when z is approaching z 0 , if and only if the boundary of D does not contain any analytic disc through z 0 in the direction of X 0 .

Generalization of a theorem of Gonchar

Let X and Y be two complex manifolds, let D⊂X and G⊂Y be two nonempty open sets, let A (resp. B) be an open subset of ∂D (resp. ∂G), and let W be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Under a geometric condition on the boundary sets A and B, we show that every function locally bounded, separately continuous on W, continuous on A×B, and separately holomorphic on (A×G)∪(D×B) “extends” to a function continuous on a “domain of holomorphy”

A new cross theorem for separately holomorphic functions

\widehat{W}

On the upper semicontinuity of the Wu metric

and holomorphic on the interior of

ON THE DEFINITION OF THE KOBAYASHI–BUSEMAN PSEUDOMETRIC

\widehat{W}