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arXiv:1208.1808 [math.AP]AbstractReferencesReviewsResources

The heat kernel on an asymptotically conic manifold

David A. Sher

Published 2012-08-09, updated 2018-12-04Version 3

In this paper, we investigate the long-time structure of the heat kernel on a Riemannian manifold M which is asymptotically conic near infinity. Using geometric microlocal analysis and building on results of Guillarmou and Hassell on the low-energy resolvent, 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.

Comments: 35 pages, 10 figures. Version 3: a result of Cheng-Li-Yau was mis-stated in the introduction, requiring minor changes in the proof of Theorem 2 on page 14, but all results still hold
Journal: Anal. PDE 6 (2013) 1755-1791
Categories: math.AP, math.SP
Subjects: 58J05, 58J35, 58J52
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