Hausdorff dimension of Markov invariant sets (Q1915553)

\textit{J. Cantwell} and \textit{L. Conlon} [Tôhoku Math. J., II. Ser. 40, 165-187 (1988; Zbl 0652.58003)] proved (among the other results) that any Markov local minimal set \({\mathcal M}\) of a codimension-one transversely orientable \(C^2\)-folition \({\mathcal F}\) of a closed manifold \(M\) has the 1-dimensional Lebesgue measure zero. In the present article, we prove slightly more: The Hausdorff dimension of such \({\mathcal M}\) satisfies \(\dim_H {\mathcal M}<1\).