Precise estimates for the subelliptic heat kernel on H-type groups
By Nathaniel Eldredge. 2008
58 citations recorded by the source corpus.
Abstract 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 − d 2 4 t ⩽ p t ⩽ C 2 Q t e − d 2 4 t , where p t is the heat kernel, and d the Carnot–Caratheodory distance on G. We also obtain similar bounds on the norm of its subelliptic gradient | ∇ p t | . Along the way, we record explicit formulas for the distance function d and the subriemannian geodesics of H-type groups.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b838b13f122a89c6ec88ab704224cc3fff4bacc2
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