The Subelliptic Heat Kernel on the CR hyperbolic spaces

Details The Subelliptic Heat Kernel on the CR hyperbolic spaces The Subelliptic Heat Kernel on the CR hyperbolic spaces

2012-04-16

arxiv.org/abs/1204.3642v1

Mathematics

Analysis of PDEs

Scientific paper

We study the heat kernel of the sub-Laplacian on the CR hyperbolic space H2n+1and on its universal covering H`2n+1. We work in cylindrical coordinates that reflects the symmetries coming from the fibration H2n+1 \rightarrow CHn, and derive an explicit and geometrically meaningful formula for the subelliptic heat kernel. As a by-product we obtain the small-time asymptotics of the heat kernel, as well as an explicit formula for the sub-Riemannian distance.

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