Year: 2026
Type: article
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 $$\mathcal {S}$$ -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.
Author: Filip Fryš
Institution: Charles University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funder: Univerzita Karlova v Praze
OpenAlex ID: W4415056034
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