The heat kernel on an asymptotically conic manifold
arXiv:1208.1808 · doi:10.2140/apde.2020.13.943
Abstract
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.
35 pages, 10 figures. Version 3: a result of Cheng-Li-Yau was mis-stated in the introduction, requiring minor changes in the proof of Theorem 2 on page 14, but all results still hold