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The Subelliptic Heat Kernel on the Anti-de Sitter Space

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Abstract

We study the subelliptic heat kernel of the sub-Laplacian on a 2n+1-dimensional anti-de Sitter space ℍ 2n+1 which also appears as a model space of a CR Sasakian manifold with constant negative sectional curvature. In particular we obtain an explicit and geometrically meaningful formula for the subelliptic heat kernel. The key idea is to work in a set of coordinates that reflects the symmetry coming from the Hopf fibration \(\mathbb{S}^{1}\to \mathbb{H}^{2n+1}\). A direct application is obtaining small time asymptotics of the subelliptic heat kernel. Also we derive an explicit formula for the sub-Riemannian distance on ℍ 2n+1.

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  1. The Institute for Mathematics and Its Applications (IMA), University of Minnesota, Minneapolis, MN, USA

    Jing Wang

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  1. Jing Wang
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Correspondence to Jing Wang.

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Wang, J. The Subelliptic Heat Kernel on the Anti-de Sitter Space. Potential Anal 45, 635–653 (2016). https://doi.org/10.1007/s11118-016-9561-2

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  • DOI: https://doi.org/10.1007/s11118-016-9561-2

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