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.
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Acknowledgements
Part of this work was carried out while the first two authors were visiting the Center of Mathematical Sciences and Applications of Harvard University. They thank the center for its hospitality and support. The authors thank Mark Kempton and Mei-Heng Yueh for some helpful discussions. The authors are also grateful to the anonymous referee for some helpful comments.
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Communicated by F.C. Marques.
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The first two authors are supported in part by the National Natural Science Foundation of China, grants 11671401, 11771136, and 11271122. The first two authors were supported in part by the Center of Mathematical Sciences and Applications (CMSA) of Harvard University. The second author is also supported by Construct Program of the Key Discipline in Hunan Province and the Hunan Province Hundred Talents Program.
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Lin, Y., Ngai, SM. & Yau, ST. Heat kernels on forms defined on a subgraph of a complete graph. Math. Ann. 380, 1891–1931 (2021). https://doi.org/10.1007/s00208-021-02215-5
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DOI: https://doi.org/10.1007/s00208-021-02215-5