Weak elastic energy of rectifiable curves in the sphere
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916946615730176 |
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| author | Mucci, Domenico Saracco, Alberto Sopio, Cristian |
| author_facet | Mucci, Domenico Saracco, Alberto Sopio, Cristian |
| contents | We introduce for any exponent $p>1$ the $p$-curvature functional for rectifiable curves in the two-dimensional sphere. We prove that this functional is finite and agrees with the integral of the geodesic curvature raised to the power $p$ on curves whose arc length parameterization is in the Sobolev class $W^{2,p}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak elastic energy of rectifiable curves in the sphere Mucci, Domenico Saracco, Alberto Sopio, Cristian Differential Geometry 53A04, 49J45 We introduce for any exponent $p>1$ the $p$-curvature functional for rectifiable curves in the two-dimensional sphere. We prove that this functional is finite and agrees with the integral of the geodesic curvature raised to the power $p$ on curves whose arc length parameterization is in the Sobolev class $W^{2,p}$. |
| title | Weak elastic energy of rectifiable curves in the sphere |
| topic | Differential Geometry 53A04, 49J45 |
| url | https://arxiv.org/abs/2509.09405 |