The subelliptic heat kernel on the CR sphere

By Fabrice Baudoin, Jing Wang. 2011

50 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c876ea86e359fa006c58f566d9aad415a6719a80

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In Applied Mathematics

1. Fabrice Baudoin
2. Davide Barilari

In Geometry and Topology

1. Fabrice Baudoin
2. Davide Barilari

Citations in the corpus

• Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations (2014, methodology): “The horizontal heat kernel was first computed in [19] that we follow but simplify since, here, the CR structure of the sphere is not relevant for us.”