Submitted Paper
Inserted: 14 jun 2025
Last Updated: 14 jun 2025
Year: 2025
Abstract:
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 distributional derivative measures of two given functions of bounded variation. The essentially unique non-smooth curve solution has both finite total curvature and total absolute torsion. In case of continuous data, we preliminarly discuss a more general problem involving a linear system of distributional derivative equations.
Keywords: functions of bounded variation, Non-smooth curves, Frenet-Serret system
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