Published Paper

Inserted: 12 sep 2025
Last Updated: 21 may 2026

Journal: Proceedings A
Year: 2025
Doi: https://doi.org/10.1098/rspa.2025.0782

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 $W^{2,p}$.

Keywords: relaxation, Curvature, elastic energy, irregular spherical curves