The strength of a geometric simplex
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915917974208512 |
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| author | Anosova, Olga Kurlin, Vitaliy |
| author_facet | Anosova, Olga Kurlin, Vitaliy |
| contents | The basic input for many real objects is a finite cloud of unordered points. The strongest equivalence between objects in practice is rigid motion in a Euclidean space. A recent polynomial-time classification of point clouds required a Lipschitz continuous function that vanishes on degenerate simplices, while the usual volume is not Lipschitz. We define the strength of any geometric simplex and prove its continuity under perturbations with explicit bounds for Lipschitz constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17630 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The strength of a geometric simplex Anosova, Olga Kurlin, Vitaliy Metric Geometry 51F20, 51N20, 51M25, 15A15 The basic input for many real objects is a finite cloud of unordered points. The strongest equivalence between objects in practice is rigid motion in a Euclidean space. A recent polynomial-time classification of point clouds required a Lipschitz continuous function that vanishes on degenerate simplices, while the usual volume is not Lipschitz. We define the strength of any geometric simplex and prove its continuity under perturbations with explicit bounds for Lipschitz constants. |
| title | The strength of a geometric simplex |
| topic | Metric Geometry 51F20, 51N20, 51M25, 15A15 |
| url | https://arxiv.org/abs/2602.17630 |