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The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3856–3891 | Cite as

The Polynomial Associated with the BFK-Gluing Formula of the Zeta-Determinant on a Compact Warped Product Manifold

  • Klaus KirstenEmail author
  • Yoonweon Lee
Article
  • 61 Downloads

Abstract

In the proof of the BFK-gluing formula of the zeta-determinant of a Laplacian there appears a polynomial of degree less than half of the dimension of an underlying manifold. This polynomial is determined completely by some data on a collar neighborhood of a cutting compact hypersurface. In this paper we compute the polynomial in terms of a warping function when a collar neighborhood of a cutting hypersurface is a warped product manifold. We also use a similar method to compute the values of a relative zeta function and a zeta function associated to the Dirichlet-to-Neumann operator at zero on a warped product manifold.

Keywords

BFK-gluing formula Relative zeta-determinant Dirichlet-to-Neumann operator Warped product metric Warping function 

Mathematics Subject Classification

Primary: 58J20 Secondary: 14F40 

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Department of MathematicsBaylor UniversityWacoUSA
  2. 2.Department of MathematicsInha UniversityIncheonKorea

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