Boundary zero-sets of A∞ functions on strictly pseudo-convex domains

1976 ◽  
pp. 17-23
Author(s):  
Anne-Marie Chollet
Keyword(s):  
Convex Domains ◽  
Zero Sets ◽  
Pseudo Convex

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.

scholarly journals Essential commutants on strongly pseudo-convex domains

2021 ◽  
Vol 280 (1) ◽  
pp. 108775
Author(s):  
Yi Wang ◽  
Jingbo Xia
Keyword(s):  
Convex Domains ◽  
Pseudo Convex

scholarly journals Zero varieties for the Nevanlinna class on all convex domains of finite type

2001 ◽  
Vol 163 ◽  
pp. 215-227 ◽  
Author(s):  
Klas Diederich ◽  
Emmanuel Mazzilli
Keyword(s):  
Finite Type ◽  
Convex Domain ◽  
Main Tool ◽  
Smooth Convex ◽  
Convex Domains ◽  
Zero Sets ◽  
Nevanlinna Class ◽  
Cauchy Riemann ◽  
Bounded Smooth

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 L1 estimate for solutions of the Cauchy-Riemann equations on such domains, which are obtained by estimating suitable kernels of Berndtsson-Andersson type.

HOLOMORPHIC NEAR INVERSES

2009 ◽  
Vol 02 (03) ◽  
pp. 417-423 ◽  
Author(s):  
Seán Dineen ◽  
Milena Venkova
Keyword(s):  
Banach Spaces ◽  
Unconditional Basis ◽  
Convex Domains ◽  
Pseudo Convex

In this article we show that holomorphic Fredholm-valued mappings defined on connected pseudo-convex domains in Banach spaces with unconditional basis always have meromorphic generalised inverses. We show they have holomorphic generalised inverses if and only if the kernels have the same dimension at all points in Ω.

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