The Gluing Formula, Conformal Scaling, and Geometry
Annals of global analysis and geometry（2021）
Abstract
We exploit conformal transformations of gluing formulas to realize connections between zeta functions of Laplacians and associated Dirichlet-to-Neumann map zeta functions. Furthermore, the geometric content in gluing formulas is identified and explicit results are given for a three-dimensional manifold.
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Key words
Regularized zeta-determinant,BFK-gluing formula,Dirichlet-to-Neumann operator,Scalar and principal curvatures,Heat trace asymptotics
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