@article {2012,
title = {On 2-step, corank 2 nilpotent sub-Riemannian metrics},
journal = {SIAM J. Control Optim., 50 (2012) 559{\textendash}582},
number = {arXiv:1105.5766;},
year = {2012},
publisher = {Society for Industrial and Applied Mathematics},
abstract = {In this paper we study the nilpotent 2-step, corank 2 sub-Riemannian metrics\\r\\nthat are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical Hausdorff measure in the case of a generic 6 dimensional, 2-step corank 2 sub-Riemannian metric.},
doi = {10.1137/110835700},
url = {http://hdl.handle.net/1963/6065},
author = {Davide Barilari and Ugo Boscain and Jean-Paul Gauthier}
}
@article {2009,
title = {The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups},
journal = {J. Funct. Anal. 256 (2009) 2621-2655},
number = {SISSA;33/2008/M},
year = {2009},
abstract = {We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation.},
doi = {10.1016/j.jfa.2009.01.006},
url = {http://hdl.handle.net/1963/2669},
author = {Andrei A. Agrachev and Ugo Boscain and Jean-Paul Gauthier and Francesco Rossi}
}
@article {2002,
title = {On the K+P problem for a three-level quantum system: optimality implies resonance},
journal = {J.Dynam. Control Systems 8 (2002),no.4, 547},
number = {SISSA;30/2002/M},
year = {2002},
publisher = {SISSA Library},
doi = {10.1023/A:1020767419671},
url = {http://hdl.handle.net/1963/1601},
author = {Ugo Boscain and Thomas Chambrion and Jean-Paul Gauthier}
}
@article {2001,
title = {On the subanalyticity of Carnot-Caratheodory distances},
journal = {Ann. I. H. Poincare - An., 2001, 18, 359},
number = {SISSA;25/00/M},
year = {2001},
publisher = {SISSA Library},
doi = {10.1016/S0294-1449(00)00064-0},
url = {http://hdl.handle.net/1963/1483},
author = {Andrei A. Agrachev and Jean-Paul Gauthier}
}