Mathematische Zeitschrift

, Volume 275, Issue 1, pp 135–150

The subelliptic heat kernel on the CR sphere

Article

DOI: 10.1007/s00209-012-1127-4

Cite this article as:
Baudoin, F. & Wang, J. Math. Z. (2013) 275: 135. doi:10.1007/s00209-012-1127-4

Abstract

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 \(\mathbb{S }^{2n+1} \rightarrow \mathbb{CP }^n\).

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

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