Heat kernel for open manifolds

It is known that for open manifolds with bounded geometry, the differential form heat kernel exists and is unique. Furthermore, it has been shown that the components of the differential form heat kernel are related via the exterior derivative and the coderivative. We will give a proof of this condit...

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Bibliographic Details
Published in:Differential geometry and its applications Vol. 28; no. 5; pp. 518 - 522
Main Author: Jones, Trevor H.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.10.2010
Subjects:
Curvature
Derivatives
Differential forms
Differential geometry
Exteriors
Green's functions
Heat kernel
Kernels
Manifolds
Mathematical analysis
Representations
Heat kernel
Differential forms
Green's functions
58J35
35K08
ISSN:0926-2245, 1872-6984
Online Access:Get full text
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Summary:It is known that for open manifolds with bounded geometry, the differential form heat kernel exists and is unique. Furthermore, it has been shown that the components of the differential form heat kernel are related via the exterior derivative and the coderivative. We will give a proof of this condition for complete manifolds with Ricci curvature bounded below, and then use it to give an integral representation of the heat kernel of degree k.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2010.02.003