The subelliptic heat kernel on the three-dimensional solvable Lie groups

Fabrice Baudoin; Matthew Cecil

doi:10.1515/forum-2013-0020

The subelliptic heat kernel on the three-dimensional solvable Lie groups

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Abstract

We study the subelliptic heat kernels of the CR three-dimensional solvable Lie groups. We first classify all left-invariant sub-Riemannian structures on three-dimensional solvable Lie groups and obtain representations of these groups. We give expressions for the heat kernels on these groups and obtain heat semigroup gradient bounds using a new type of curvature-dimension inequality.

Original language	English
Journal	Forum Mathematicum
Volume	27
Issue	4
Pages (from-to)	2051-2086
Number of pages	36
ISSN	0933-7741
DOIs	https://doi.org/10.1515/forum-2013-0020
Publication status	Published - 1 Jul 2015
Externally published	Yes

Keywords

curvature-dimension inequality
solvable Lie group
sub-Riemannian geometry
Subelliptic heat kernel

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10.1515/forum-2013-0020

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AU - Cecil, Matthew

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AB - We study the subelliptic heat kernels of the CR three-dimensional solvable Lie groups. We first classify all left-invariant sub-Riemannian structures on three-dimensional solvable Lie groups and obtain representations of these groups. We give expressions for the heat kernels on these groups and obtain heat semigroup gradient bounds using a new type of curvature-dimension inequality.

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KW - solvable Lie group

KW - sub-Riemannian geometry

KW - Subelliptic heat kernel

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The subelliptic heat kernel on the three-dimensional solvable Lie groups

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Keywords

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