Global regularity for the \(\overline{\partial}_b\)-equation on \(C R\) manifolds of arbitrary codimension. (English) Zbl 1470.32102

Summary: Let \(M\) be a \(\mathcal{C}^{\infty}\) compact \(C R\) manifold of \(C R\)-codimension \(\ell \geq 1\) and \(C R\)-dimension \(n - \ell\) in a complex manifold \(X\) of complex dimension \(n \geq 3\). In this paper, assuming that \(M\) satisfies condition \(Y(s)\) for some \(s\) with \(1 \leq s \leq n - \ell - 1\), we prove an \(L^2\)-existence theorem and global regularity for the solutions of the tangential Cauchy-Riemann equation for \((0, s)\)-forms on \(M\).


32V05 CR structures, CR operators, and generalizations
32W10 \(\overline\partial_b\) and \(\overline\partial_b\)-Neumann operators
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
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