The analyticity of \(q\)-concave sets of locally finite \((2n-2q)\)-dimensional Hausdorff measure
In the context of finding reasonable assumptions on a closed subset \(A\) of an analytic space \(X\) in order to guarantee that \(A\) is itself analytic, the paper is devoted to the proof of the following result: If \(X\) is a complex space of pure dimension \(n\), \(q\) is a positive integer less than \(n\) and \(A\) is a \(q\)-concave subset in \(X\) whose Hausdorff \((2n-2q)\)-measure is locally finite, then \(A\) is analytic of pure dimension \(n-q\). A relation with the notion of \(q\)- pseudoconcavity considered by \textit{M. Peternell} in [Invent. Math. 85, 249-262 (1986; Zbl 0599.32016)] is also presented.
scientific article; zbMATH DE number 1478819