Weak elastic energy of rectifiable curves in the sphere
Abstract 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 W2,p.
Authors
- Domenico Mucci (ORCID: https://orcid.org/0000-0001-7459-3740)
- Alberto Saracco (ORCID: https://orcid.org/0000-0001-5776-4747)
- Cristian Sopio (ORCID: https://orcid.org/0009-0002-4996-4209)
Institutions
- University of Parma (IT)
- University of Ferrara (IT)
Publication Details
- Journal
- Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
- Published
- 2026-04-15
- DOI
- https://doi.org/10.1098/rspa.2025.0782
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 0.00