We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable
surfaces for which a local orthonormal frame is given by a pair of vector fields that can …

This is the first paper of a series in which we plan to study spectral asymptotics for sub-
Riemannian (sR) Laplacians and to extend results that are classical in the Riemannian case …

For an equiregular sub-Riemannian manifold M, Popp's volume is a smooth volume which is
canonically associated with the sub-Riemannian structure, and it is a natural generalization …

Nous établissons le développement asymptotique en temps petit de noyaux de la chaleur d’opérateurs
de Hörmander hypoelliptiques au voisinage de la diagonale, généralisant des résultats …

For a sub-Riemannian manifold provided with a smooth volume, we relate the small-time
asymptotics of the heat kernel at a point y of the cut locus from $ x $ with roughly" how much" …

We study topological aspects of defect modes for a family of operators P (t), obtained as a
Schrödinger operator P0 perturbed by a phase defect t between−∞ and+∞: a dislocation …

We study spectral properties of sub-Riemannian Laplacians, which are hypoelliptic
operators. The main objective is to obtain quantum ergodicity results, what we have …

We study the heat kernel of the sub-Laplacian L on the CR sphere S^ 2n+ 1. An explicit and
geometrically meaningful formula for the heat kernel is obtained. As a by-product we recover …

We generalize the results of Montgomery (Commun Math Phys 168: 651–675, 1995) for the
Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann …

Swimming consists by definition in propelling through a fluid by means of bodily movements.
Thus, from a mathematical point of view, swimming turns into a control problem for which the …