Tohoku Mathematical Journal
2020
June
SECOND SERIES VOL. 72, NO. 2

Tohoku Math. J.
72 (2020), 261-282

Title A FORMULA FOR THE HEAT KERNEL COEFFICIENTS ON RIEMANNIAN MANIFOLDS

Author Masayoshi Nagase

(Received April 13, 2018)
Abstract. Based on the idea of adiabatic expansion theory, we will present a new formula for the asymptotic expansion coefficients of every derivative of the heat kernel on a compact Riemannian manifold. It will be very useful for having systematic understanding of the coefficients, and, furthermore, by using only a basic knowledge of calculus added to the formula, one can describe them explicitly up to an arbitrarily high order.

Mathematics Subject Classification. Primary 58J35; Secondary 58J37, 70H11.
Key words and phrases. Heat kernel, asymptotic expansion, adiabatic expansion.

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