The subelliptic heat kernel on the CR sphere

We study the heat kernel of the sub-Laplacian on the CR sphere . 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 that was obtained by Geller (J Differ Geom 15:417–435, 1980...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 275; no. 1-2; pp. 135 - 150
Main Authors Baudoin, Fabrice, Wang, Jing
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2013
Subjects
Mathematics
Mathematics and Statistics
Steep Descent Method
Heat Kernel
Beltrami Operator
North Pole
Order Differential Operator
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Summary:We study the heat kernel of the sub-Laplacian on the CR sphere . 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 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 .
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-012-1127-4