The fundamental theorem of the local theory for non-smooth curves

Domenico Mucci; Alberto Saracco

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arXiv · 2506.12564

The fundamental theorem of the local theory for non-smooth curves

Domenico Mucci·Alberto Saracco

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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.

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Domenico Mucci, Alberto Saracco. 2025-06-14. The fundamental theorem of the local theory for non-smooth curves. https://arxiv.org/abs/2506.12564

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