10 research outputs found
Global Regularity for the ∂
Let M be a C∞ compact CR manifold of CR-codimension l≥1 and CR-dimension n-l in a complex manifold X of complex dimension n≥3. In this paper, assuming that M satisfies condition Y(s) for some s with 1≤s≤n-l-1, we prove an L2-existence theorem and global regularity for the solutions of the tangential Cauchy-Riemann equation for (0,s)-forms on M
Holomorphic Approximation on Certain Weakly Pseudoconvex Domains in Cn
The purpose of this paper is to study the Mergelyan approximation property in L p and C k -scales on certain weakly pseudoconvex domains of finite/infinite type in C n . At the heart of our results lies the solvability of the additive Cousin problem with bounds as well as estimates of the ∂ ¯ -equation in the corresponding topologies
-regularity for the -equation with a support condition
summary:Let be a -convex intersection, , , in a complex manifold of complex dimension , , and let be a holomorphic vector bundle of rank over . In this paper, -estimates, , for solutions to the \hbox {-equation} with small loss of smoothness are obtained for -valued -forms on when . In addition, we solve the -equation with a support condition in -spaces. More precisely, we prove that for a -closed form in , , , with compact support and for with there exists a form in with compact support such that in . Applications are given for a separation theorem of Andreotti-Vesentini type in -setting and for the solvability of the -equation for currents
Global solutions with C^k-estimates for bar-d-equations on q-concave intersections
We construct a global solution to the -equation with -estimates on q-concave intersections in . Our main tools are integral formulas