This analysis introduces a p-curvature functional, assessing geodesic curvature in curves on a sphere, suggesting new insights into elastic energies.
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.
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Mucci et al. (2026) studied this question.
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