Is there an explicit formula in the literature for the heat kernel of the Hodge Laplacian on differential forms?
I found some on functions, but not on forms of higher degree.
What at least about 1-forms on the hyperbolic plane?
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asked Jun 10, 2015 at 16:43
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$\begingroup$ There is a formula for the heat kernel of Hodge Laplacian on noncompact type semisimple symmetric space $G/K$, given by Harish-Chandra. The formula is written down by Plancherel density, which is explicit for the hyperbolic space $SO_0(n,1)/SO(n)$. Maybe this formula is not very explicit as what you want, but enough for some applications. See theorem 2.2 in math.uiuc.edu/documenta/vol-07/11.pdf $\endgroup$– shuCommented Jun 11, 2015 at 10:14
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