Klas Diederich

Pseudoconvex domains of semiregular type

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.

Sharp hölder estimates for\(\overline \partial \) on ellipsoids

AbstractWe solve the

Smoothingq-convex functions in the singular case

\overline \partial

A smooth pseudoconvex domain without pseudoconvex exhaustion

-equation on real and on complex ellipsoids in ℂN. It is proved that the solution satisfies sharp Hölder estimates. That is, the Hölder exponent equals the reciprocal of the maximal order of contact of the boundary of the ellipsoid with complex-analytic curves.

Geometric and analytic boundary invariants on pseudoconvex domains. Comparison results

Abstract. It is shown, that the so-called Blaschke condition characterizes in any bounded smooth convex domain of finite type exactly the divisors which are zero sets of functions of the Nevanlinna class on the domain. The main tool is a non-isotropic L estimate for solutions of the Cauchy-Riemann equations on such domains, which are obtained by estimating suitable kernels of BerndtssonAndersson type.

Open sets with Stein hypersurface sections in Stein spaces

Definition 1. Let f2 be a complex space, ~ : f 2 ~ R a continuous function, and q > 1 an integer. Then a) Q is called q-convex (in the C~~ sense), if for each point p c f2 there is a local coordinate patch U on 62 with a holomorphic embedding z : U ~ t) for some open set U C C N and a C ~ (strongly) q-convex function ~ on V such that ~1U=~ o i. b) 0 is called q-convex with corners if for each p c f2 there is an open neighborhood U C f2 and on U finitely many q-convex functions (in the C ~~ sense) Q1 . . . . . Q~ such that QI U = max{01 . . . . . Qz}.

A remark on a paper by S.R. Bell

It is shown that the exact -∞-sets of plurisubharmonic functions are not necessarily complex-analytic even if they are closed C -smooth real submanifolds.

A characterization of the ball in ℂn

A pseudoconvex demain with real —analytic smooth boundary on a complex manifold is constructed which cannot be exhausted by pseudoconvex domains.