A. Agrachev, D. Barilari, and U. Boscain, On the Hausdorff volume in sub-Riemannian geometry, Calc. Var. Partial Differential Equations, vol.43, issue.3-4, pp.355-388, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00672260

A. Agrachev, D. Barilari, and U. Boscain, A Comprehensive Introduction to Sub-Riemannian geometry, Cambridge Studies in Advanced Mathematics, vol.181, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02019181

A. Agrachev, U. Boscain, J. Gauthier, and F. Rossi, The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups, J. Funct. Anal, vol.256, issue.8, pp.2621-2655, 2009.

A. Agrachev and A. Marigo, Rigid Carnot algebras: a classification, J. Dyn. Control Syst, vol.11, issue.4, pp.449-494, 2005.

D. Barilari, Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry, Translation of Sovrem. Mat. Prilozh, vol.195, issue.3, pp.391-411, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00672262

A. Bellaïche, The tangent space in sub-Riemannian geometry, Sub-Riemannian geometry, vol.144, pp.1-78, 1996.

G. Ben and A. , Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale, Ann. Inst. Fourier (Grenoble), vol.39, issue.1, pp.73-99, 1989.

G. Ben-arous and R. Léandre, Décroissance exponentielle du noyau de la chaleur sur la diagonale. I. Probab. Theory Related Fields, vol.90, pp.175-202, 1991.

G. Ben-arous and R. Léandre, Décroissance exponentielle du noyau de la chaleur sur la diagonale, vol.90, pp.377-402, 1991.

J. Bony, Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés, Ann. Inst. Fourier (Grenoble), vol.19, issue.1, pp.277-304, 1969.

J. Cheeger, M. Gromov, and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom, vol.17, issue.1, pp.15-53, 1982.

Y. Colin-de-verdière, L. Hillairet, and E. Trélat, Spectral asymptotics for sub-Riemannian Laplacians II: equiregular structures, Grushin and Martinet cases

Y. Colin-de-verdière, L. Hillairet, and E. Trélat, Spectral asymptotics for sub-Riemannian Laplacians, III: general singular structures

Y. Colin-de-verdière, L. Hillairet, and E. Trélat, Quantum ergodicity and quantum limits for sub-Riemannian Laplacians, Séminaire Laurent Schwartz-Équations aux dérivées partielles et applications. Année, 2014.

Y. Colin-de-verdière, L. Hillairet, and E. Trélat, Spectral asymptotics for sub-Riemannian Laplacians, I: Quantum ergodicity and quantum limits in the 3-dimensional contact case, Duke Math. J, vol.167, issue.1, pp.109-174, 2018.

T. Coulhon and A. Sikora, Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem, Proc. Lond. Math. Soc, vol.96, issue.3, pp.507-544, 2008.

J. , P. Eckmann, and M. Hairer, Spectral properties of hypoelliptic operators, Comm. Math. Phys, vol.235, issue.2, pp.233-253, 2003.

K. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics, vol.194, 2000.

K. Fukaya, Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Invent. Math, vol.87, issue.3, pp.517-547, 1987.

Z. Ge, Collapsing Riemannian metrics to Carnot-Carathéodory metrics and Laplacians to sub-Laplacians, Canad. J. Math, vol.45, issue.3, pp.537-553, 1993.

M. Gromov, Carnot-Carathéodory spaces seen from within, Sub-Riemannian geometry, vol.144, pp.79-323, 1996.

B. Helffer and F. Nier, Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians, Lecture Notes in Mathematics, vol.1862, 2005.

L. Hörmander, On the division of distributions by polynomials, Ark. Mat, vol.3, pp.555-568, 1958.

L. Hörmander, Hypoelliptic second order differential equations, Acta Math, vol.119, pp.147-171, 1967.

E. P. Hsu, On the principle of not feeling the boundary for diffusion processes, J. London Math. Soc, vol.51, issue.2, pp.373-382, 1995.

D. Huet, Phénomènes de perturbation singulière dans les problèmes aux limites, Ann. Inst. Fourier. Grenoble, vol.10, pp.61-150, 1960.

F. Jean, Control of nonholonomic systems: from sub-Riemannian geometry to motion planning, Springer Briefs in Mathematics, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01137580

D. S. Jerison and A. Sánchez-calle, Estimates for the heat kernel for a sum of squares of vector fields, Indiana Univ. Math. J, vol.35, issue.4, pp.835-854, 1986.

Y. Kannai, Off diagonal short time asymptotics for fundamental solutions of diffusion equations, Commun. Partial Differ. Equations, vol.2, issue.8, pp.781-830, 1977.

J. J. Kohn, Pseudo-differential operators and hypoellipticity, Partial differential equations (Proc. Sympos, vol.XXIII, pp.61-69, 1971.

S. Kusuoka and D. W. Stroock, Long time estimates for the heat kernel associated with a uniformly subelliptic symmetric second order operator, Ann. of Math, vol.127, issue.2, pp.165-189, 1988.

E. Le-donne, Lecture Notes on sub-Riemannian geometry, Lecture Notes. Ongoing work, 2017.

J. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lecture Notes in Mathematics, vol.323, 1973.

P. Maheux, Estimations du noyau de la chaleur sur les espaces homogènes, J. Geom. Anal, vol.8, issue.1, pp.65-96, 1998.

A. Marigo, Classification of Carnot algebras: the semi-rigid cases, J. Dyn. Control Syst, vol.13, issue.1, pp.95-119, 2007.

R. Melrose, The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two, J. Analyse Math, vol.44, p.85, 1984.

A. Menikoff and J. Sjöstrand, On the eigenvalues of a class of hypoelliptic operators, Math. Ann, vol.235, issue.1, pp.55-85, 1978.

G. Métivier, Fonction spectrale et valeurs propres d'une classe d'opérateurs non elliptiques, Comm. Partial Differential Equations, vol.1, issue.5, pp.467-519, 1976.

R. Montgomery, A tour of subriemannian geometries, their geodesics and applications, Mathematical Surveys and Monographs, vol.91, 2002.

A. Pazy, Semigroups of linear operators and applications to partial differential equations, 1983.

L. Rifford, Sub-Riemannian geometry and optimal transport, Springer Briefs in Mathematics, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01131787

M. Rumin, Sub-Riemannian limit of the differential form spectrum of contact manifolds, Geom. Funct. Anal, vol.10, issue.2, pp.407-452, 2000.

L. Saloff-coste, A note on Poincaré, Sobolev, and Harnack inequalities, Internat. Math. Res. Notices, issue.2, pp.27-38, 1992.

A. Sánchez-calle, Fundamental solutions and geometry of the sum of squares of vector fields, Invent. Math, vol.78, issue.1, pp.143-160, 1984.

R. S. Strichartz, Sub-Riemannian geometry, J. Differential Geom, vol.24, issue.2, pp.221-263, 1986.

N. Th and . Varopoulos, Small time Gaussian estimates of heat diffusion kernels. II. The theory of large deviations, J. Funct. Anal, vol.93, issue.1, pp.1-33, 1990.