\(C^\infty\) extensions of holomorphic functions from subvarieties of a convex domain (Q2756093)

The author obtains the \(C^\infty\) boundary regularity of extension functions from a subvariety of a convex domain: Let \(\Omega\subset\mathbb C^n\) be a bounded convex domain with \(C^\infty\) boundary. Let \(M\) be a subvariety of \(\Omega\) of dimension \(m\) which intersects \(\partial\Omega\) transversally. Suppose that \(\Omega\) is totally convex at any point of \(\partial M\) in the complex tangential directions. Let \(f\in\mathcal O(M)\cap C^\infty(\overline M)\). Then there exists a holomorphic function \(F\in\mathcal O(\Omega)\cap C^\infty(\overline\Omega)\) such that \(F(z) = f(z)\) for \(z\in M\).