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Über die 1. und 2. Ableitungen der Bergmanschen Kernfunktion und ihr Randverhalten.

Klas Diederich — 1973

Mathematische Annalen

Über Gebiete mit vollständiger Kählermetrik.

Klas Diederich; Peter Pflug — 1981

Mathematische Annalen

A Levi Problem on Two-Dimensional Complex Manifolds.

Klas Diederich; Takeo Ohsawa — 1982

Mathematische Annalen

Strange complex structures on Euclidean space.

Klas Diederich; Nessim Sibony — 1979

Journal für die reine und angewandte Mathematik

Extension and restriction of holomorphic functions

Klas Diederich; Emmanuel Mazzilli — 1997

Annales de l'institut Fourier

Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds $D^{'}$ of pseudoconvex domains $D$ to all of $D$ even in quite simple situations; The spaces $A^{p} (D^{'}) : = 𝒪 (D^{'}) \cap L^{p} (D^{'})$ are, in general, not at all preserved. Also the image of the Hilbert space $A^{2} (D)$ under the restriction to $D^{'}$ can have a very strange structure.

Quantitative estimates for the Green function and an application to the Bergman metric

Klas Diederich; Gregor Herbort — 2000

Annales de l'institut Fourier

Let $D \subset ℂ^{n}$ be a bounded pseudoconvex domain that admits a Hölder continuous plurisubharmonic exhaustion function. Let its pluricomplex Green function be denoted by $G_{D} (., .)$ . In this article we give for a compact subset $K \subset D$ a quantitative upper bound for the supremum ${sup}_{z \in K} | G_{D} (z, w) |$ in terms of the boundary distance of $K$ and $w$ . This enables us to prove that, on a smooth bounded regular domain $D$ (in the sense of Diederich-Fornaess), the Bergman differential metric $B_{D} (w; X)$ tends to infinity, for $X \in ℂ^{n} / {O}$ , when $w \in D$ tends to a boundary point....

Real and complex analytic sets. The relevance of Segre varieties

Klas Diederich; Emmanuel Mazzilli — 2008

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $X \subset {ℂ^{n}}^{n}$ be a closed real-analytic subset and put $𝒜 : = {z \in X ∣ \exists A \subset X, germ of a complex-analytic set, z \in A, {dim}_{z} A > 0}$ This article deals with the question of the structure of $𝒜$ . In the main result a natural proof is given for the fact, that $𝒜$ always is closed. As a main tool an interesting relation between complex analytic subsets of $X$ of positive dimension and the Segre varieties of $X$ is proved and exploited.