Complete characterization of anisotropic geodesics in the Euclidean space
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914029093519360 |
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| author | Aldrigo, Pietro |
| author_facet | Aldrigo, Pietro |
| contents | Let $F$ be a lower semicontinuous, 1-homogeneous positive function defined on $\mathbf{R}^n$. We provide a characterization of absolutely continuous paths that minimize the anisotropic $F$-length between two points. The characterization is achieved by establishing a connection between the minimizing paths and the geometry of the anisotropic $F$-isoperimetric set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete characterization of anisotropic geodesics in the Euclidean space Aldrigo, Pietro Classical Analysis and ODEs Differential Geometry 49K21, 49Q10, 51M25 Let $F$ be a lower semicontinuous, 1-homogeneous positive function defined on $\mathbf{R}^n$. We provide a characterization of absolutely continuous paths that minimize the anisotropic $F$-length between two points. The characterization is achieved by establishing a connection between the minimizing paths and the geometry of the anisotropic $F$-isoperimetric set. |
| title | Complete characterization of anisotropic geodesics in the Euclidean space |
| topic | Classical Analysis and ODEs Differential Geometry 49K21, 49Q10, 51M25 |
| url | https://arxiv.org/abs/2509.07224 |