#### Vol. 6, No. 7, 2013

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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