Abstract
In this paper, we study the small time asymptotics for the heat kernel on a sub-Riemannian manifold, using a perturbative approach. We explicitly compute, in the case of a 3D contact structure, the first two coefficients of the small time asymptotics expansion of the heat kernel on the diagonal, expressing them in terms of the two basic functional invariants χand κ defined on a 3D contact structure.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 82, Nonlinear Control and Singularities, 2012.
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Barilari, D. Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry. J Math Sci 195, 391–411 (2013). https://doi.org/10.1007/s10958-013-1585-1
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DOI: https://doi.org/10.1007/s10958-013-1585-1