scholarly journals Global Regularity for the∂-b-Equation onCRManifolds of Arbitrary Codimension

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Shaban Khidr ◽  
Osama Abdelkader
Keyword(s):  
Existence Theorem ◽  
Complex Manifold ◽  
Global Regularity ◽  
Riemann Equation ◽  
Complex Dimension ◽  
Arbitrary Codimension ◽  
Cauchy Riemann ◽  
Tangential Cauchy Riemann Equation

LetMbe aC∞compactCRmanifold ofCR-codimensionl≥1andCR-dimensionn-lin a complex manifoldXof complex dimensionn≥3. In this paper, assuming thatMsatisfies conditionY(s)for someswith1≤s≤n-l-1, we prove anL2-existence theorem and global regularity for the solutions of the tangential Cauchy-Riemann equation for(0,s)-forms onM.

scholarly journals On holomorphic extension of functions on singular real hypersurfaces inℂn

2001 ◽  
Vol 26 (3) ◽  
pp. 173-178
Author(s):  
Tejinder S. Neelon
Keyword(s):  
Limit Point ◽  
Infinite Order ◽  
Holomorphic Extension ◽  
Real Hypersurfaces ◽  
Zero Set ◽  
Riemann Equation ◽  
Real Analytic ◽  
Cauchy Riemann ◽  
Extension Of Functions ◽  
Tangential Cauchy Riemann Equation

The holomorphic extension of functions defined on a class of real hypersurfaces inℂnwith singularities is investigated. Whenn=2, we prove the following: everyC1function onΣthat satisfies the tangential Cauchy-Riemann equation on boundary of{(z,w)∈ℂ2:|z|k<P(w)},P∈C1,P≥0andP≢0, extends holomorphically inside provided the zero setP(w)=0has a limit point orP(w)vanishes to infinite order. Furthermore, ifPis real analytic then the condition is also necessary.

SUR L'ÉQUATION DE CAUCHY–RIEMANN TANGENTIELLE DANS UNE CALOTTE STRICTEMENT PSEUDOCONVEXE

2005 ◽  
Vol 16 (09) ◽  
pp. 1063-1079 ◽  
Author(s):  
CHRISTINE LAURENT-THIÉBAUT
Keyword(s):  
Stein Manifold ◽  
Geometrical Characterization ◽  
Riemann Equation ◽  
Pseudoconvex Boundary ◽  
Cauchy Riemann ◽  
Tangential Cauchy Riemann Equation

We search a cohomological and a geometrical characterization of the open subsets of a strictly pseudoconvex boundary in a Stein manifold on which one can solve the tangential Cauchy–Riemann equation in all bidegrees. On cherche une caractérisation cohomologique et géométrique des ouverts du bord d'un domaine strictement pseudoconvexe relativement compact d'une variété de Stein sur lesquels on peut résoudre l'équation de Cauchy–Riemann tangentielle en tout bidegré.

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