Precise Estimates for the Subelliptic Heat Kernel on H-type Groups

Details Precise Estimates for the Subelliptic Heat Kernel on H-type Groups Precise Estimates for the Subelliptic Heat Kernel on H-type Groups

2008-10-17

arxiv.org/abs/0810.3218v2

Mathematics

Analysis of PDEs

49 pages, no figures. Submitted to Journal de Math\'ematiques Pures et Appliqu\'ees. Version history: v1 submit bbl file so bi

Scientific paper

We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups G of H-type. Specifically, we show that there exist positive constants C_1, C_2 and a polynomial correction function Q_t on G such that C_1 Q_t e^{-\frac{d^2}{4t}} \le p_t \le C_2 Q_t e^{-\frac{d^2}{4t}}, where p_t is the heat kernel, and d the Carnot-Carath\'eodory distance on G. We also obtain similar bounds on the norm of its subelliptic gradient |\nabla p_t|. Along the way, we record explicit formulas for the distance function d and the subriemannian geodesics of H-type groups.

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