PreprintCC BY 4.0arXiv
Carnot geodesics with Hölder controls
Abstract
We construct an explicit length-minimizing curve in a polynomial rank-two sub-Riemannian structure on R4. Its arclength parametrization is C1,1/2 and is not C1,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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BibTeX
@misc{cavallucci2026carnot,
title = {{Carnot geodesics with Hölder controls}},
author = {Nicola Cavallucci and Enrico Le Donne and Sebastiano Nicolussi Golo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38481},
eprint = {2610.38481},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38481},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Carnot geodesics with Hölder controls
AU - Nicola Cavallucci
AU - Enrico Le Donne
AU - Sebastiano Nicolussi Golo
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38481
UR - https://arxiv.org/abs/2610.38481
AB - 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.
ER -