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arXiv · 2503.01373

Tangency sets of non-involutive distributions and unrectifiability in Carnot-Carath\'{e}odory spaces

Giovanni Alberti·Annalisa Massaccesi·Andrea Merlo
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Abstract

In this paper, we establish refined versions of the Frobenius Theorem for non-involutive distributions and use these refinements to prove an unrectifiability result for Carnot-Carath\'{e}odory spaces. We also introduce a new class of metric spaces that extends the framework of Carnot-Carath\'{e}odory geometry and show that, within this class, Carnot-Carath\'{e}odory spaces are, in some sense, extremal. Our results provide new insights into the relationship between integrability, non-involutivity, and rectifiability in both classical and sub-Riemannian settings.

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Giovanni Alberti, Annalisa Massaccesi, Andrea Merlo. 2025-03-03. Tangency sets of non-involutive distributions and unrectifiability in Carnot-Carath\'{e}odory spaces. https://arxiv.org/abs/2503.01373

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