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math.DG2025
Weak elastic energy of rectifiable curves in the sphere
Domenico Mucci, Alberto Saracco, Cristian Sopio
We introduce for any exponent the -curvature functional for rectifiable curves in the two-dimensional sphere. We prove that this functional is finite and agrees with the i…
math.DG2025
The fundamental theorem of the local theory for non-smooth curves
Domenico Mucci, Alberto Saracco
We extend the classical fundamental theorem of the local theory of smooth curves to a wider class of non-smooth data. Curvature and torsion are prescribed in terms of the distribut…