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The heat kernel on an asymptotically conic manifold

In this paper, we investigate the long-time structure of the heat kernel on a Riemannian manifold M which is asymptotically conic near infinity. Using geometric microlocal analysis and building on results of Guillarmou and Hassell on the low-energy resolvent, we give a complete description of the asymptotic structure of the heat kernel in all spatial and temporal regimes. We apply this structure to define and investigate a renormalized zeta function and determinant of the Laplacian on M.