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

2006 ◽  
Vol 85 (1) ◽  
pp. 71-118 ◽  
Author(s):  
Philippe Charpentier ◽  
Yves Dupain
Keyword(s):  
Finite Type ◽  
Bergman Kernel ◽  
Levi Form ◽  
Convex Domains ◽  
Pseudo Convex

ON DISCONTINUITY OF THE BERGMAN KERNEL FUNCTION

1999 ◽  
Vol 10 (07) ◽  
pp. 825-832
Author(s):  
KLAS DIEDERICH ◽  
GREGOR HERBORT
Keyword(s):  
Finite Type ◽  
Kernel Function ◽  
Real Line ◽  
Bergman Kernel ◽  
Pseudoconvex Domain ◽  
Convex Domains ◽  
Bergman Kernel Function ◽  
Finite Type Domains

Let [Formula: see text] be a Ck-smoothly (with k≥1) bounded pseudoconvex domain and [Formula: see text] denote its Bergman kernel function. In this article the question is investigated, whether the function [Formula: see text] is continuous up to the boundary in the topology of the extended real line [Formula: see text]. We give two counterexamples: one in the class of finite type domains with k = ∞ and one in the class of convex domains with k = 1.

Zero Varieties for the Nevanlinna Class in Convex Domains of Finite Type in \Bbb C n

1998 ◽  
Vol 147 (2) ◽  
pp. 391 ◽  
Author(s):  
Joaquim Bruna ◽  
Philippe Charpentier ◽  
Yves Dupain
Keyword(s):  
Finite Type ◽  
Convex Domains ◽  
Nevanlinna Class

scholarly journals Gain of Regularity in Extension Problem on Convex Domains

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
M. Jasiczak
Keyword(s):  
Finite Type ◽  
Bergman Space ◽  
Bergman Spaces ◽  
Extension Problem ◽  
Convex Domains

We investigate the extension problem from higher codimensional linear subvarieties on convex domains of finite type. We prove that there exists a constantdsuch that on Bergman spacesHp(D)with1≤p<dthere appears the so-called “gain regularity.” The constantddepends on the minimum of the dimension and the codimension of the subvariety. This means that the space of functions which admit an extension to a function in the Bergman spaceHp(D)is strictly larger thanHp(D∩A), whereAis a subvariety.

Coupled Vortex Equations on Complete Kähler Manifolds

2008 ◽  
Vol 51 (3) ◽  
pp. 467-480
Author(s):  
Yue Wang
Keyword(s):  
Symmetric Spaces ◽  
Existence Results ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Convex Domains ◽  
Hermitian Symmetric Spaces ◽  
Vortex Equations ◽  
Curved Manifolds ◽  
Pseudo Convex ◽  
Simply Connected

AbstractIn this paper, we first investigate the Dirichlet problem for coupled vortex equations. Secondly, we give existence results for solutions of the coupled vortex equations on a class of complete noncompact Kähler manifolds which include simply-connected strictly negative curved manifolds, Hermitian symmetric spaces of noncompact type and strictly pseudo-convex domains equipped with the Bergmann metric.

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