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arXiv · 2509.06545

Anisotropic lower-dimensional Minkowski content and $\mathcal{S}$-content

Filip Fryš
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Abstract

This paper investigates the lower-dimensional anisotropic Minkowski content and $\mathcal{S}$-content. We establish that these anisotropic contents exhibit properties analogous to their isotropic counterparts by proving analogous inequalities between the lower-dimensional anisotropic Minkowski content and $\mathcal{S}$-content. A key component of our approach is demonstrating that the associated anisotropic volume function is of Kneser type, a result that underpins many of our proofs. In addition, we introduce anisotropic versions of the Minkowski and $\mathcal{S}$-dimensions and derive inequalities relating them. As an application, we analyze the existence of the $\log_2(3)$-dimensional anisotropic Minkowski and $\mathcal{S}$-contents of the Sierpinski gasket.

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Filip Fryš. 2025-09-08. Anisotropic lower-dimensional Minkowski content and $\mathcal{S}$-content. https://doi.org/10.1007/s10231-025-01650-4

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