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The heat kernel on an
asymptotically conic manifold
David A. Sher |
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Vol. 6 (2013), No. 7, 1755–1791
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Abstract |
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We investigate the long-time structure of the heat kernel on a Riemannian manifold 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 . |
Keywords
heat kernel, asymptotically conic manifold, zeta function,
determinant of the Laplacian
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Mathematical Subject Classification 2010
Primary: 58J05, 58J35, 58J52
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Milestones
Received: 9 August 2012
Revised: 17 April 2013
Accepted: 13 May 2013
Published: 27 December 2013
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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 |
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