The asymptotic expansion for the trace of the heat kernel on a generalized surface of revolution
Ping Charng Lue
Trans. Amer. Math. Soc. 273 (1982), 93-110
Primary 58G11; Secondary 35K05
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Abstract: Let be a smooth compact Riemannian manifold without boundary. Let be an open interval. Let be a smooth positive function. Let be the metric on . Consider the fundamental solution of the heat equation on with metric (when exists globally we call it the heat kernel on ). The coefficients of the asymptotic expansion of the trace are studied and expressed in terms of corresponding coefficients on the basis . It is fulfilled by means of constructing a parametrix for which is different from a parametrix in the standard form. One important result is that each of the former coefficients is a linear combination of the latter coefficients.
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