The heat kernel on an asymptotically conic manifold
Analysis of PDEs
2020-04-22 v3 Spectral Theory
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.
Cite
@article{arxiv.1208.1808,
title = {The heat kernel on an asymptotically conic manifold},
author = {David A. Sher},
journal= {arXiv preprint arXiv:1208.1808},
year = {2020}
}
Comments
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