Vol. 6, No. 7, 2013

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 2, 309–612
Issue 1, 1–308

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
Other MSP Journals
The heat kernel on an asymptotically conic manifold

David A. Sher

Vol. 6 (2013), No. 7, 1755–1791

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.

heat kernel, asymptotically conic manifold, zeta function, determinant of the Laplacian
Mathematical Subject Classification 2010
Primary: 58J05, 58J35, 58J52
Received: 9 August 2012
Revised: 17 April 2013
Accepted: 13 May 2013
Published: 27 December 2013
David A. Sher
Department of Mathematics and Statistics
McGill University
805 Sherbrooke Street West
Montréal QC  H3A 2K6
Centre de Recherches Mathématiques
Université de Montréal
CP 6128 succursale Centre-Ville
Montréal QC  H3C 3J7