The fundamental theorem of the local theory for non-smooth curves
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909649210441728 |
|---|---|
| author | Mucci, Domenico Saracco, Alberto |
| author_facet | Mucci, Domenico Saracco, Alberto |
| contents | We extend the classical fundamental theorem of the local theory of smooth curves to a wider class of non-smooth data. Curvature and torsion are prescribed in terms of the distributional derivative measures of two given functions of bounded variation. The essentially unique non-smooth curve solution has both finite total curvature and total absolute torsion. In case of continuous data, we preliminarly discuss a more general problem involving a linear system of distributional derivative equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The fundamental theorem of the local theory for non-smooth curves Mucci, Domenico Saracco, Alberto Differential Geometry 53A04, 26A45, 49J45 We extend the classical fundamental theorem of the local theory of smooth curves to a wider class of non-smooth data. Curvature and torsion are prescribed in terms of the distributional derivative measures of two given functions of bounded variation. The essentially unique non-smooth curve solution has both finite total curvature and total absolute torsion. In case of continuous data, we preliminarly discuss a more general problem involving a linear system of distributional derivative equations. |
| title | The fundamental theorem of the local theory for non-smooth curves |
| topic | Differential Geometry 53A04, 26A45, 49J45 |
| url | https://arxiv.org/abs/2506.12564 |