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The subelliptic heat kernel on the CR sphere

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 $$\mathbb{S }^{2n+1} \rightarrow \mathbb{CP }^n$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

The subelliptic heat kernel on the CR sphere

Mathematische Zeitschrift , Volume 275 (2) – Dec 8, 2012

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References (20)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-012-1127-4
Publisher site
See Article on Publisher Site

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

Journal

Mathematische ZeitschriftSpringer Journals

Published: Dec 8, 2012

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