Extension of CR-functions from piecewise smooth CR-manifolds

This article is devoted to the locally polynomially convex hull of a CR-manifold. 1) An “edge of the wedge” type theorem is obtained for piecewise smooth CR-manifolds in $\mathbf C^n$. 2) It is shown that a CR-manifold of class $C^1$ is locally polynomially convex if and only if in a neighborhood of each point it foliates into complex analytic submanifolds of maximal possible dimension. 3) It is shown that only locally polynomially convex CR-manifolds are examples of manifolds on which the tangential Cauchy–Riemann equations $\overline\partial u=f$ are solvable locally for any $\overline\partial$-closed form $f$.
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