The heat kernel on an asymptotically conic manifold

Abstract

We investigate the long-time structure of the heat kernel on a Riemannian manifold $M$ that is asymptotically conic near infinity. Using geometric microlocal analysis and building on results of Guillarmou and Hassell, 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 $M$.