A counterexample to uniform approximation on totally real manifolds in \(\mathbb C^{3}\) (Q1045741)

The author constructs an example, which proves the following theorem: There exists a proper \(\mathbb{C}^{\infty}\)-smooth embedding \(\phi: \mathbb{R}^{2} \rightarrow \mathbb{C}^{3}\) such that \(M:=\phi(\mathbb{R}^{2})\) is totally real and polynomially convex and yet \(M\) does not admit uniform approximation.