1 June 2006 Regularized determinants of Laplace-type operators, analytic surgery, and relative determinants
Jörn Müller, Werner Müller
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Duke Math. J. 133(2): 259-312 (1 June 2006). DOI: 10.1215/S0012-7094-06-13323-9


Let M be a compact Riemannian manifold in which Y is an embedded hypersurface separating M into two parts. Assume that the metric is a product on a tubular neighborhood N of Y. Let Δ be a Laplace-type operator on M adapted to the product structure on N. Under certain additional assumptions on Δ, we establish an asymptotic expansion for the logarithm of the regularized determinant detΔ of Δ if the tubular neighborhood N is stretched to a cylinder of infinite length. We use the asymptotic expansions to derive adiabatic splitting formulas for regularized determinants


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Jörn Müller. Werner Müller. "Regularized determinants of Laplace-type operators, analytic surgery, and relative determinants." Duke Math. J. 133 (2) 259 - 312, 1 June 2006. https://doi.org/10.1215/S0012-7094-06-13323-9


Published: 1 June 2006
First available in Project Euclid: 21 May 2006

zbMATH: 1111.58026
MathSciNet: MR2225693
Digital Object Identifier: 10.1215/S0012-7094-06-13323-9

Primary: 58J52
Secondary: 58J50

Rights: Copyright © 2006 Duke University Press

Vol.133 • No. 2 • 1 June 2006
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