The \(n\)-dimensional gradient has the 1-dimensional Denjoy-Clarkson property (Q1803976)

The author proves the following result: Let \(f: \Omega\to\mathbb{R}\) be a differentiable function, where \(\Omega\subset\mathbb{R}^ n\) is open, then the set \((\nabla f)^{-1}(G)\) is either empty or has positive 1-dimensional Hausdorff measure. The present result is connected to a conjecture of \textit{C. E. Weil} [Real Anal. Exch. 16, No. 1, 373 (1991)].