Global Regularity for the ∂ - b -Equation on C R Manifolds of Arbitrary Codimension

Abstract EN

Let M be a C ∞ compact C R manifold of C R -codimension l ≥ 1 and C R -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 L 2 -existence theorem and global regularity for the solutions of the tangential Cauchy-Riemann equation for ( 0 , s ) -forms on M .