Weak elastic energy of rectifiable curves in the sphere

Domenico Mucci; Alberto Saracco; Cristian Sopio

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arXiv · 2509.09405

Weak elastic energy of rectifiable curves in the sphere

Domenico Mucci·Alberto Saracco·Cristian Sopio

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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 $W^{2,p}$.

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Domenico Mucci, Alberto Saracco, Cristian Sopio. 2025-09-11. Weak elastic energy of rectifiable curves in the sphere. https://arxiv.org/abs/2509.09405

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