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arXiv · 2610.38481

Carnot geodesics with Hölder controls

Nicola Cavallucci·Enrico Le Donne·Sebastiano Nicolussi Golo
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Abstract

We construct an explicit length-minimizing curve in a polynomial rank-two sub-Riemannian structure on $\R^4$. Its arclength parametrization is $C^{1,1/2}$ and is not $C^{1,α}$ near an interior point for any $α>1/2$. Minimality is proved by an approximate calibration chosen separately for each competitor. The example admits a minimizing lift to a rank-two Carnot group of step five. Generalizations are announced.

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Nicola Cavallucci, Enrico Le Donne, Sebastiano Nicolussi Golo. 2026-10-28. Carnot geodesics with Hölder controls. https://arxiv.org/abs/2610.38481

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