Open Access
Issue |
ESAIM: COCV
Volume 28, 2022
|
|
---|---|---|
Article Number | 9 | |
Number of page(s) | 28 | |
DOI | https://doi.org/10.1051/cocv/2021104 | |
Published online | 27 January 2022 |
- A. Agrachev, D. Barilari and U. Boscain, A Comprehensive Introduction to Sub-Riemannian Geometry. Cambridge Studies in Advanced Mathematics. Cambridge University Press (2019). [Google Scholar]
- A. Agrachev, U. Boscain and M. Sigalotti, A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds. Discr. Continu. Dyn. Syst. A 20 (2008) 801–822. [CrossRef] [Google Scholar]
- A.A. Andronov, E.A. Leontovich, I.I. Gordon and A.G. Maier, Qualitative Theory of Second Order Dynamic Systems. Israel Program for Scientific Trasnlations Ltd. (1973). [Google Scholar]
- S.K. Aranson, G.R. Belitsky and E. Zhuzhoma, Introduction to the Qualitative Theory of Dynamical Systems on Surfaces. Vol. 153 of Translations of Mathematical Monographs. American Mathematical Society (1996). [CrossRef] [Google Scholar]
- N. Arcozzi and F. Ferrari, Metric normal and distance function in the Heisenberg group. Math. Zeitsch. 256 (2007) 661–684. [CrossRef] [Google Scholar]
- N. Arcozzi and F. Ferrari, The Hessian of the distance from a surface in the Heisenberg group. Ann. Acad. Sci. Fennicae. Math. 33 (2008) 35–63. [MathSciNet] [Google Scholar]
- Z.M. Balogh, Size of characteristic sets and functions with prescribed gradient. J. für die Reine Angew. Math. [Crelle’s Journal] 564 (2003) 63–83. [Google Scholar]
- Z.M. Balogh, J.T. Tyson and E. Vecchi, Intrinsic curvature of curves and surfaces and a Gauss–Bonnet theorem in the Heisenberg group. Math. Zeitsch. 287 (2017) 1–38. [CrossRef] [Google Scholar]
- D. Barilari, I. Beschastnyi and A. Lerario, Volume of small balls and sub-Riemannian curvature in 3D contact manifolds. J. Symplectic Geom. 18 (2020). [Google Scholar]
- D. Barilari, U. Boscain, D. Cannarsa and K. Habermann, Stochastic processes on surfaces in three-dimensional contact sub-Riemannian manifolds. Preprint arXiv e-print (2020). [Google Scholar]
- D. Bennequin, Entrelacements et équations de Pfaff., in IIIe rencontre de géométrie du Schnepfenried, 10-15 mai 1982. Vol. 1: Feuilletages. Géométrie symplectique et de contact. Analyse non standard et applications. Astérisqué 107/108 (1983) 87–161. [Google Scholar]
- A. Bressan, Tutorial on the center manifold theorem. Lecture Notes in Mathematics. Springer Verlag, Germany (2007). [CrossRef] [Google Scholar]
- D. Burago, Y. Burago and S. Ivanov, A course in metric geometry. Vol. 33 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2001). [Google Scholar]
- L. Capogna, D. Danielli, S. Pauls and J. Tyson, An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem. Vol. 259 of Progress in Mathematics. Birkhäuser Verlag, Basel (2007). [Google Scholar]
- D. Danielli, N. Garofalo and D.-M. Nhieu, Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces. Mem. Am. Math. Soc. 182 (2006). [Google Scholar]
- D. Danielli, N. Garofalo and D.M. Nhieu, Sub-Riemannian calculus on hypersurfaces in Carnot groups. Adv. Math. 215 (2007) 292–378. [CrossRef] [MathSciNet] [Google Scholar]
- D. Danielli, N. Garofalo and D.-M. Nhieu, Integrability of the sub-Riemannian mean curvature of surfaces in the Heisenberg group. Proc. Am. Math. Soc. 140 (2012). [Google Scholar]
- M.M. Diniz and J.M.M. Veloso, Gauss-Bonnet theorem in sub-Riemannian Heisenberg space H1 . J. Dyn. Control Syst. 22 (2016) 807–820. [CrossRef] [MathSciNet] [Google Scholar]
- J.B. Etnyre, Introductory lectures on contact geometry. Topol. Geometry Manifolds (2003) 81–107. [CrossRef] [Google Scholar]
- H. Geiges, An Introduction to Contact Topology, Cambridge Studies in Advanced Mathematics. Cambridge University Press (2008). [Google Scholar]
- E. Giroux, Convexité en topologie de contact. Commentarii mathematici Helvetici 66 (1991) 637–677. [CrossRef] [MathSciNet] [Google Scholar]
- E. Giroux, Structures de contact en dimension trois et bifurcations des feuilletages de surfaces. Invent. Math. 141 (2000) 615–689. [CrossRef] [MathSciNet] [Google Scholar]
- M. Gromov, Carnot-Carathéodory spaces seen from within. Edited by A. Bellaïche and J.-J. Risler. Progress in Mathematics, vol. 144, Birkhäuser Basel, Basel (1996). [Google Scholar]
- M. Guysinsky, B. Hasselblatt and V. Rayskin, Differentiability of the Hartman–Grobman linearization. Discr. Continu. Dyn. Syst. 9 (2003) 979–984. [CrossRef] [Google Scholar]
- P. Hartman, On local homeomorphisms of Euclidean space. Boletin de la Sociedad Matematica Mexicana 5 (1960) 220–241. [Google Scholar]
- F. Jean, Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning. SpringerBriefs in Mathematics Springer International Publishing (2014). [Google Scholar]
- P.W.Y. Lee, On surfaces in three dimensional contact manifolds. Can. J. Math. 65 (2013) 621–633. [CrossRef] [Google Scholar]
- R. Montgomery, A Tour of sub-Riemannian Geometries, Their Geodesics and Applications. Mathematical surveys and monographs. American Mathematical Society (2002). [Google Scholar]
- S.D. Pauls, Minimal surfaces in the Heisenberg group. Geometriae Dedicata 104 (2004) 201–231. [CrossRef] [MathSciNet] [Google Scholar]
- L. Perko, Differential Equations and Dynamical Systems. Texts in Applied Mathematics. Springer, New York (2012). [Google Scholar]
- L. Rifford, Sub-Riemannian Geometry and Optimal Transport. SpringerBriefs in Mathematics. Springer International Publishing (2014). [CrossRef] [Google Scholar]
- L. Rizzi and T. Rossi, Heat content asymptotics for sub-Riemannian manifolds. J. Math. Pures Appl. 148 (2021) 267–307. [CrossRef] [MathSciNet] [Google Scholar]
- K. Tan and X. Yang, On some sub-riemannian objects in hypersurfaces of sub-riemannian manifolds. Bull. Aust. Math. Soc. 70 (2004) 177–198. [CrossRef] [Google Scholar]
- J. Veloso, Limit of Gaussian and normal curvatures of surfaces in Riemannian approximation scheme for sub-Riemannian three dimensional manifolds and Gauss-Bonnet theorem. Preprint arXiv e-print (2020). [Google Scholar]
- Y. Wang and S. Wei, Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane. Sci. China Math. (2020). [Google Scholar]
- I. Zelenko and M. Zhitomirskii, Rigid paths of generic 2-distributions on 3-manifolds. Duke Math. J. 79 (1995). [CrossRef] [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.