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.

Locations

• Analysis & PDE - View - PDF
• arXiv (Cornell University) - View - PDF
• Project Euclid (Cornell University) - View - PDF