Hypoelliptic heat kernel on 3-step nilpotent Lie groups

Details Hypoelliptic heat kernel on 3-step nilpotent Lie groups Hypoelliptic heat kernel on 3-step nilpotent Lie groups

2010-02-03

arxiv.org/abs/1002.0688v1

Mathematics

Analysis of PDEs

Scientific paper

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 that permits to transform the hypoelliptic heat equation in a one dimensional heat equation with a quartic potential.

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