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- Title
Hypoelliptic Heat Kernel Over 3-Step Nilpotent Lie Groups.
- Authors
Boscain, U.; Gauthier, J.-P.; Rossi, F.
- Abstract
In this paper, we provide explicitly the connection between the hypoelliptic heat kernel for some 3-step sub-Riemannian manifolds and the quartic oscillator. We study the left-invariant sub-Riemannian structure on two nilpotent Lie groups, namely, the (2,3,4) group (called the Engel group) and the (2,3,5) group (called the Cartan group or the generalized Dido problem). Our main technique is noncommutative Fourier analysis, which permits us to transform the hypoelliptic heat equation into a one-dimensional heat equation with a quartic potential.
- Subjects
HYPOELLIPTIC differential equations; HEAT equation; KERNEL functions; NILPOTENT Lie groups; MATHEMATICAL transformations; FOURIER analysis
- Publication
Journal of Mathematical Sciences, 2014, Vol 199, Issue 6, p614
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-014-1889-9