Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 72
Number of page(s) 24
DOI https://doi.org/10.1051/cocv/2024058
Published online 07 October 2024
  1. A. Bonfiglioli, E. Lanconelli and F. Uguzzoni, Stratified Lie groups and potential theory for their sub-Laplacians. Springer Monographs in Mathematics. Springer, Berlin (2007). [Google Scholar]
  2. A. Agrachev, D. Barilari and U. Boscain, A comprehensive introduction to sub-Riemannian geometry, Cambridge Studies in Advanced Mathematics, Vol. 181. Cambridge University Press, Cambridge (2020), from the Hamiltonian viewpoint, With an appendix by Igor Zelenko. [Google Scholar]
  3. H. Reiter, Uber den Satz von Wiener und lokalkompakte Gruppen. Comment. Math. Helv. 49 (1974) 333–364. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.F. Torres Lopera, Geodesics and conformal transformations of Heisenberg-Reiter spaces. Trans. Am. Math. Soc. 306 (1988) 489–498. [CrossRef] [Google Scholar]
  5. A. Martini, Spectral multipliers on Heisenberg-Reiter and related groups. Ann. Mat. Pura Appl. 194 (2015) 1135–1155. [CrossRef] [MathSciNet] [Google Scholar]
  6. C. Autenried and M.G. Molina, The sub-Riemannian cut locus of H-type groups. Math. Nachr. 289 (2016) 4–12. [CrossRef] [MathSciNet] [Google Scholar]
  7. A. Agrachev, D. Barilari and U. Boscain, On the Hausdorff volume in sub-Riemannian geometry. Calc. Var. Partial Diff. Equ. 43 (2012) 355–388. [CrossRef] [Google Scholar]
  8. D. Barilari, U. Boscain and J.-P. Gauthier, On 2-step, corank 2, nilpotent sub-Riemannian metrics. SIAM J. Control Optim. 50 (2012) 559–582. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Montanari and D. Morbidelli, On the subRiemannian cut locus in a model of free two-step Carnot group. Calc. Var. Partial Diff. Equ. 56 (2017) Paper No. 36, 26. [CrossRef] [Google Scholar]
  10. O. Myasnichenko, Nilpotent (3, 6) sub-Riemannian problem. J. Dynam. Control Syst. 8 (2002) 573–597. [CrossRef] [Google Scholar]
  11. L. Rizzi and U. Serres, On the cut locus of free, step two Carnot groups. Proc. Am. Math. Soc. 145 (2017) 5341–5357. [CrossRef] [Google Scholar]
  12. Yu.L. Sachkov, Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions. Uspekhi Mat. Nauk 77 (2022) 109–176. MR 4461360 [CrossRef] [Google Scholar]
  13. H.-Q. Li, The Carnot-Caratheodory distance on 2-step groups. arXiv:2112.07822 (2021). [Google Scholar]
  14. H.-Q. Li and Y. Zhang, Sub-Riemannian geometry on some step-two Carnot groups, arXiv:2102.09860 (2021). [Google Scholar]
  15. C. Meyer, Matrix Analysis and Applied Linear Algebra. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2000), with 1 CD-ROM (Windows, Macintosh and UNIX) and a solutions manual (iv+171 pp.). [CrossRef] [Google Scholar]
  16. W.P.A. Klingenberg, Riemannian Geometry, 2nd edn. De Gruyter Studies in Mathematics, Vol. 1. Walter de Gruyter & Co., Berlin (1995). [CrossRef] [Google Scholar]
  17. F.W. Warner, The conjugate locus of a Riemannian manifold. Am. J. Math. 87 (1965) 575–604. [CrossRef] [Google Scholar]
  18. L. Rifford and E. Trelat, On the stabilization problem for nonholonomic distributions. J. Eur. Math. Soc. 11 (2009) 223–255. [CrossRef] [MathSciNet] [Google Scholar]
  19. G.W. Stewart, On the continuity of the generalized inverse. SIAM J. Appl. Math. 17 (1969) 33–45. MR 245583 [CrossRef] [MathSciNet] [Google Scholar]
  20. A.A. Agrachev and Y.L. Sachkov, Control theory from the geometric viewpoint. Encyclopaedia of Mathematical Sciences, Vol. 87. Springer-Verlag, Berlin (2004), Control Theory and Optimization, II. [CrossRef] [Google Scholar]
  21. A. Montanari and D. Morbidelli, On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups. J. Math. Anal. Appl. 444 (2016) 1652–1674. [CrossRef] [MathSciNet] [Google Scholar]
  22. L. Ambrosio and S. Rigot, Optimal mass transportation in the Heisenberg group. J. Funct. Anal. 208 (2004) 261–301. [CrossRef] [MathSciNet] [Google Scholar]
  23. P. Hajlasz and S. Zimmerman, Geodesics in the Heisenberg group. Anal. Geom. Metr. Spaces 3 (2015) 325–337. MR 3417082 [MathSciNet] [Google Scholar]
  24. R. Monti, Some properties of Carnot-Caratheodory balls in the Heisenberg group. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 11 (2000) 155–167. [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.