References
- Grushin VV. On a class of hypoelliptic operators. Math Sb. 1970;83(125):456–473.
- Grushin VV. A certain class of elliptic pseudodifferential operators that are degenerate on a submanifold. Math Sb. 1971;84(126):163–195.
- Calin O, Chang DC. Sub-riemannian geometry: general theory and exemples. Vol. 126, Cambridge: Cambridge University Press; 2009. (EMIA).
- Varadhan SRS. On the behaviour of the fundamental solution of the heat equation with variable coefficients. Commun Pure Appl Math. 1967;20:431–455.
- Fefferman C, Sanchez-Calle A. Fundamental solutions for second order subelliptic operators. Ann Math. 1986;124(2):247–272.
- Chang DC, Li Y. SubRiemannian geodesics in the Grushin plane. J Geom Anal. 2012;22:800–826.
- Chang CH, Chang DC, Gaveau B, et al. Geometric analysis on a step 2 Grushin operator. Bull Inst Math Acad Sinica (New Series). 2009;4(2):119–188.
- Hörmander L. Hypoelliptic second order differential operators. Acta Math. 1967;119:147–171.
- Beals R, Gaveau B, Greiner PC. Hamilton--Jacobi theory and the heat kernel on Heisenberg groups. J Math Pures Appl. 2000;79(7):633–689.
- Bellaïche A, Risler JJ. Sub-riemannian geometry. Basel: Birkhäuser; 1996. (Progress in mathematics; Vol. 144).
- Montgomery R. A tour of subriemannian geometries, their geodesics and applications. Providence (RI): AMS; 2002. (Math surveys and monographs; Vol. 91).
- Vranceanu G. Sur les spaces non holonomes. C R Acad Sci Paris. 1926;183(1):852–854.
- Vranceanu G. Leçons de Géométrie Différentielle. Bucharest: Rotativa; 1947.
- Gromow M. Carnot--Carathéodory spaces seen from within. In: Bellaïche A, Risler J.J., editors. Sub-Riemannian geometry. Basel: Birkhäuser; 1996. (Progress in mathematics; Vol. 144).
- Chow WL. Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung. Math Ann. 1939;177:98–105.
- Rashevskii PK. About connecting two points of complete nonholonomic space by admissible curve. Uch Zapiski Ped Instit K Liebknechta. 1938;2:83–94.
- Calin O,Chang DC, Greiner PC, et al. On the geometry induced by a Grushin operator. In: Complex analysis and dynamical systems II. Providence (RI): American Mathematical Society; 2005; p. 89–111. (Contemporary Mathematics; 382).
- Gaveau B. Principle de moindre action, propagation de la chaleur et estimeems sous elliptiques sur certains groups nilpotents. Acta Math. 1977;139:95–153.
- Gaveau B, Greiner P. On geodesics in subRiemannian geometry. Bull Inst Math Acad Sinica (New Series). 2006;1:79–209.