Vol. 6, No. 7, 2013

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
The heat kernel on an asymptotically conic manifold

David A. Sher

Vol. 6 (2013), No. 7, 1755–1791
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.

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