A nonremovable generic 4-ball in the unit sphere of \(\mathbb{C}^3\)
A compact \(K\Subset S^{2n-1}\) in the unit sphere of \(\mathbb{C}^n\) is called removable if any continuous (but not necessarily bounded) function \(f\) on \(S^{2n-1}\setminus K\), which satisfies there the tangential Cauchy-Riemann equation \(\overline\partial_bf=0\), extends to an analytic function in the unit ball \(B^{2n}\). The main result of the paper is an example of the smooth generic 4-ball \(B^4\) in \(S^5\subset\mathbb{C}^3\) which is not removable. I.e. there exists an imbedding \(\varphi:B^4\to S^5\) such that the CR-dimension of \(\varphi (B^4)\) is one at every point and there exists an entire function \(f\) in \(\mathbb{C}^3\) such that its zero set \(X\) intersects \(S^5\) transversally and \(X\cap \overline B^6\subset \varphi(B^4)\).
scientific article; zbMATH DE number 1437629