The BFK type gluing formula of zeta-determinants for the Robin Boundary condition

Author:

Klaus Kirsten, Yoonweon Lee

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-06-29 16:00:00

Abstract

In this paper we discuss the BFK type gluing formula for zeta-determinants of Laplacians with respect to the Robin boundary condition on a compact Riemannian manifold. As a special case, we discuss the gluing formula with respect to the Neumann boundary condition. We also compute the difference of two zeta-determinants with respect to the Robin and Dirichlet boundary conditions. We use this result to compute the zeta-determinant of a Laplacian on a cylinder when the Robin boundary condition is imposed, which extends a result in [25]. We also discuss the gluing formula more precisely when the product structure is given near a cutting hypersurface.

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