Heat kernels on forms defined on a subgraph of a complete graph

Yong Lin; Sze Man Ngai; Shing Tung Yau

doi:10.1007/s00208-021-02215-5

Heat kernels on forms defined on a subgraph of a complete graph

Yong Lin, Sze Man Ngai, Shing Tung Yau

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We study the heat kernel expansion of the Laplacian on n-forms defined on a subgraph of a directed complete graph. We derive two expressions for the subgraph heat kernel on 0-forms and compute the coefficients of the expansion. We also obtain the subgraph heat kernel of the Laplacian on 1-forms.

Original language	English
Pages (from-to)	1891-1931
Number of pages	41
Journal	Mathematische Annalen
Volume	380
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-021-02215-5
State	Published - Aug 2021

Keywords

Heat kernel
Laplacian
n-forms; complete graph

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10.1007/s00208-021-02215-5

Cite this

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title = "Heat kernels on forms defined on a subgraph of a complete graph",

abstract = "We study the heat kernel expansion of the Laplacian on n-forms defined on a subgraph of a directed complete graph. We derive two expressions for the subgraph heat kernel on 0-forms and compute the coefficients of the expansion. We also obtain the subgraph heat kernel of the Laplacian on 1-forms.",

keywords = "Heat kernel, Laplacian, n-forms; complete graph",

author = "Yong Lin and Ngai, {Sze Man} and Yau, {Shing Tung}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Lin, Yong

AU - Ngai, Sze Man

AU - Yau, Shing Tung

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N2 - We study the heat kernel expansion of the Laplacian on n-forms defined on a subgraph of a directed complete graph. We derive two expressions for the subgraph heat kernel on 0-forms and compute the coefficients of the expansion. We also obtain the subgraph heat kernel of the Laplacian on 1-forms.

AB - We study the heat kernel expansion of the Laplacian on n-forms defined on a subgraph of a directed complete graph. We derive two expressions for the subgraph heat kernel on 0-forms and compute the coefficients of the expansion. We also obtain the subgraph heat kernel of the Laplacian on 1-forms.

KW - Heat kernel

KW - Laplacian

KW - n-forms; complete graph

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DO - 10.1007/s00208-021-02215-5

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EP - 1931

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

Heat kernels on forms defined on a subgraph of a complete graph

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Keywords

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