Global Solvability and Regularity for $\overline\partial$ on an Annulus Between Two Weakly Pseudo-Convex Domains

1985 ◽  
Vol 291 (1) ◽  
pp. 255 ◽  
Author(s):  
Mei-Chi Shaw
Keyword(s):  
Global Solvability ◽  
Convex Domains ◽  
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

Global solvability and regularity for ∂¯ on an annulus between two weakly convex domains which satisfy property (P)

2019 ◽  
Vol 12 (03) ◽  
pp. 1950041
Author(s):  
Sayed Saber
Keyword(s):  
Neumann Problem ◽  
Complex Manifold ◽  
Global Solvability ◽  
Closed Formula ◽  
Convex Domains ◽  
Weakly Convex ◽  
Canonical Solution ◽  
Dimension Formula ◽  
Satisfy Property

Let [Formula: see text] be a complex manifold of dimension [Formula: see text] and let [Formula: see text]. Let [Formula: see text] be a weakly [Formula: see text]-convex and [Formula: see text] be a weakly [Formula: see text]-convex in [Formula: see text] with smooth boundaries such that [Formula: see text]. Assume that [Formula: see text] and [Formula: see text] satisfy property [Formula: see text]. Then the compactness estimate for [Formula: see text]-forms [Formula: see text] holds for the [Formula: see text]-Neumann problem on the annulus domain [Formula: see text]. Furthermore, if [Formula: see text] is [Formula: see text]-closed [Formula: see text]-form, which is [Formula: see text] on [Formula: see text] and which is cohomologous to zero on [Formula: see text], the canonical solution [Formula: see text] of the equation [Formula: see text] is smooth on [Formula: see text].

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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