The BFK-gluing formula for zeta-determinants and the conformal rescaling of a metric

DOI10.1007/978-3-030-75425-9_15zbMath1501.58018OpenAlexW3211772383MaRDI QIDQ2066119

Yoonweon Lee, Klaus Kirsten

Publication date: 13 January 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-75425-9_15

zbMATH Keywords

Dirichlet-to-Neumann operatorsgluing formulazeta-determinantsconformal rescaling

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Index theory and related fixed-point theorems on manifolds (58J20) Pseudodifferential and Fourier integral operators on manifolds (58J40) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Determinants and determinant bundles, analytic torsion (58J52)

Cites Work

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• Spectral functions, special functions and the Selberg zeta function
• Mayer-Vietoris type formula for determinants of elliptic differential operators
• The polynomial associated with the BFK-gluing formula of the zeta-determinant on a compact warped product manifold
• Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems
• The spectral zeta function for Laplace operators on warped product manifolds of the type \(I \times _{f } N\)
• Heat invariants of the Steklov problem
• Asymptotic expansion of the trace of the heat kernel associated to the Dirichlet-to-Neumann operator
• Regularized determinants of Laplace-type operators, analytic surgery, and relative determinants
• The BFK-gluing formula and relative determinants on manifolds with cusps
• The BFK-gluing formula and the curvature tensors on a 2-dimensional compact hypersurface
• The Burghelea-Friedlander-Kappeler–gluing formula for zeta-determinants on a warped product manifold and a product manifold
• Determining anisotropic real-analytic conductivities by boundary measurements
• Determinant relatif et la fonction XI
• Mayer-Vietoris Formulas for the Determinant of a Laplace Operator on a Even-Dimensional Manifold

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