#### 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