Conformal perturbation of heat kernels and their traces (Q1816712)

The authors summary: ``On a compact \(n\)-dimensional Riemannian manifold \(M\) we consider self-adjoint operators of type \(w^{-1}\Delta\) acting on \(L^2(M,wdx)\), where \(dx\) is the volume element of \(M\) and \(w>0\) is smooth. For \(n=2\) this setup arises naturally from a conformal change of metric. We derive perturbation series for the heat kernel of these operators and their traces, in terms of \(w\) and of objects in the given background metric. The method involves Gaussian estimates on space and time derivatives of the complex time heat kernel''.