2023/06/30 by Klaus Kirsten, Kirsten, Klaus, Yoonweon Lee +1 · 1 citation
Computer Science · Mathematics · #58J20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2306.17572
openalex publication_date 2023/06/30 · openalex created_date 2023/07/05 · openalex updated_date 2026/07/28
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.