Submitted Paper

Inserted: 12 sep 2025
Last Updated: 12 sep 2025

Year: 2025

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 $W^{2,p}$.