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

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

5 Citationer (Scopus)

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.

Originalsprog	Engelsk
Tidsskrift	Forum Mathematicum
Vol/bind	27
Nummer	4
Sider (fra-til)	2051-2086
Antal sider	36
ISSN	0933-7741
DOI	https://doi.org/10.1515/forum-2013-0020
Status	Udgivet - 1 jul. 2015
Udgivet eksternt	Ja

Adgang til dokumentet

10.1515/forum-2013-0020

Andre filer og links

Link to publication in Scopus

Citationsformater

@article{23a13543b13f4292b09c68ba249d60b0,

title = "The subelliptic heat kernel on the three-dimensional solvable Lie groups",

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.",

keywords = "curvature-dimension inequality, solvable Lie group, sub-Riemannian geometry, Subelliptic heat kernel",

author = "Fabrice Baudoin and Matthew Cecil",

note = "Publisher Copyright: {\textcopyright} 2015 by De Gruyter.",

year = "2015",

month = jul,

day = "1",

doi = "10.1515/forum-2013-0020",

language = "English",

volume = "27",

pages = "2051--2086",

journal = "Forum Mathematicum",

issn = "0933-7741",

publisher = "Walter de Gruyter GmbH",

number = "4",

}

TY - JOUR

T1 - The subelliptic heat kernel on the three-dimensional solvable Lie groups

AU - Baudoin, Fabrice

AU - Cecil, Matthew

PY - 2015/7/1

Y1 - 2015/7/1

N2 - 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.

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.

KW - curvature-dimension inequality

KW - solvable Lie group

KW - sub-Riemannian geometry

KW - Subelliptic heat kernel

UR - http://www.scopus.com/inward/record.url?scp=84935492279&partnerID=8YFLogxK

U2 - 10.1515/forum-2013-0020

DO - 10.1515/forum-2013-0020

M3 - Journal article

AN - SCOPUS:84935492279

SN - 0933-7741

VL - 27

SP - 2051

EP - 2086

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 4

ER -

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

Abstract

Adgang til dokumentet

Andre filer og links

Fingeraftryk

Citationsformater