Geometry of pseudo-convex domains of finite type with locally diagonalizable Levi form and Bergman kernel

In this paper, we give a precise description of the complex geometry of a pseudo-convex domain in C n near a boundary point of finite type where the Levi form is locally diagonalizable, and we use it to obtain sharp size estimates for the Bergman kernel and its derivatives. When all points of the bo...

Full description

Saved in:
Bibliographic Details
Published in:Journal de mathématiques pures et appliquées Vol. 85; no. 1; pp. 71 - 118
Main Authors: Charpentier, Philippe, Dupain, Yves
Format: Journal Article
Language:English
Published: Paris Elsevier SAS 2006
Elsevier
Subjects:
Bergman kernel
Complex Variables
Convex and discrete geometry
Exact sciences and technology
Finite type
Functions of a complex variable
Geometry
Mathematical analysis
Mathematics
Plurisubharmonic functions
Sciences and techniques of general use
Several complex variables and analytic spaces
Bergman kernel
Finite type
Plurisubharmonic functions
Complex geometry
Complex domain
Convex geometry
Kernel estimation
Plurisubharmonic function
Regularity
Bergman kemel
ISSN:0021-7824
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we give a precise description of the complex geometry of a pseudo-convex domain in C n near a boundary point of finite type where the Levi form is locally diagonalizable, and we use it to obtain sharp size estimates for the Bergman kernel and its derivatives. When all points of the boundary are of that type, we deduce from those estimates the L p regularity of the Bergman projection. On donne une description précise de la géométrie complexe d'un domaine pseudo-convexe de C n au voisinage d'un point du bord de type fini où la forme de Levi est localement diagonalisable. On utilise cette description pour établir des estimations fines du noyau de Bergman ainsi que de ses dérivées. De ces estimations on déduit la régularité L p du projecteur de Bergman lorsque tous les points du bord ont la propriété considérée.
ISSN:0021-7824
DOI:10.1016/j.matpur.2005.10.001