Geodesic
Local heat kernel
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 136-152

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The paper is devoted to a local heat kernel, which is a special component of the standard heat kernel. Localization means that all considerations are performed in an open convex subset of a smooth Riemannian manifold. We discuss such properties and concepts as uniqueness, a symmetry of the Seeley–DeWitt coefficients, extension to the entire manifold, a family of special functions, and the late-time asymptotic behavior using the path integral approach. 
@article{ZNSL_2024_532_a6,
     author = {A. V. Ivanov},
     title = {Local heat kernel},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {136--152},
     publisher = {mathdoc},
     volume = {532},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a6/}
}
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A. V. Ivanov. Local heat kernel. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 136-152. http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a6/