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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2509.06545 |
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| _version_ | 1866917205997780992 |
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| author | Fryš, Filip |
| author_facet | Fryš, Filip |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anisotropic lower-dimensional Minkowski content and $\mathcal{S}$-content Fryš, Filip Classical Analysis and ODEs 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. |
| title | Anisotropic lower-dimensional Minkowski content and $\mathcal{S}$-content |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2509.06545 |