Page 1

Displaying 1 – 3 of 3

Showing per page

On boundary behaviour of the Bergman projection on pseudoconvex domains

M. Jasiczak (2005)

Studia Mathematica

It is shown that on strongly pseudoconvex domains the Bergman projection maps a space L v k of functions growing near the boundary like some power of the Bergman distance from a fixed point into a space of functions which can be estimated by the consecutive power of the Bergman distance. This property has a local character. Let Ω be a bounded, pseudoconvex set with C³ boundary. We show that if the Bergman projection is continuous on a space E L ( Ω ) defined by weighted-sup seminorms and equipped with the topology...

On regular Stein neighborhoods of a union of two totally real planes in ℂ²

Tadej Starčič (2016)

Annales Polonici Mathematici

We find regular Stein neighborhoods of a union of totally real planes M = (A+iI)ℝ² and N = ℝ² in ℂ², provided that the entries of a real 2 × 2 matrix A are sufficiently small. A key step in our proof is a local construction of a suitable function ρ near the origin. The sublevel sets of ρ are strongly Levi pseudoconvex and admit strong deformation retraction to M ∪ N.

On the automorphism group of strongly pseudoconvex domains in almost complex manifolds

Jisoo Byun, Hervé Gaussier, Kang-Hyurk Lee (2009)

Annales de l’institut Fourier

In contrast with the integrable case there exist infinitely many non-integrable homogeneous almost complex manifolds which are strongly pseudoconvex at each boundary point. All such manifolds are equivalent to the Siegel half space endowed with some linear almost complex structure.We prove that there is no relatively compact strongly pseudoconvex representation of these manifolds. Finally we study the upper semi-continuity of the automorphism group of some hyperbolic strongly pseudoconvex almost...

Currently displaying 1 – 3 of 3

Page 1