| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 70 | |
| Number of page(s) | 30 | |
| DOI | https://doi.org/10.1051/cocv/2023055 | |
| Published online | 18 August 2023 | |
Derivatives of Sub-Riemannian Geodesics are Lp-Hölder Continuous*
1
Steklov Mathematical Institute of Russian Academy of Sciences, Russia
2
Lomonosov Moscow State University, Russia
** Corresponding author: lion.lokut@gmail.com
Received:
1
April
2022
Accepted:
19
July
2023
This article is devoted to the long-standing problem on the smoothness of sub-Riemannian geodesics. We prove that the derivatives of sub-Riemannian geodesics are always Lp-Hölder continuous. Additionally, this result has several interesting implications. These include (i) the decay of Fourier coefficients on abnormal controls, (ii) the rate at which they can be approximated by smooth functions, (iii) a generalization of the Poincaré inequality, and (iv) a compact embedding of the set of shortest paths into the space of Bessel potentials.
Mathematics Subject Classification: 53C17 / 49J15
Key words: Sub-Riemannian geometry / abnormal geodesic / Besov spaces / interpolation theory / convex duality problem
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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