Mathematische Zeitschrift

, Volume 275, Issue 1–2, pp 135–150

The subelliptic heat kernel on the CR sphere



We study the heat kernel of the sub-Laplacian \(L\) on the CR sphere \(\mathbb{S }^{2n+1}\). An explicit and geometrically meaningful formula for the heat kernel is obtained. As a by-product we recover in a simple way the Green function of the conformal sub-Laplacian \(-L+n^2\) that was obtained by Geller (J Differ Geom 15:417–435, 1980), and also get an explicit formula for the sub-Riemannian distance. The key point is to work in a set of coordinates that reflects the symmetries coming from the fibration \(\mathbb{S }^{2n+1} \rightarrow \mathbb{CP }^n\).


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

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