The gluing formula, conformal scaling, and geometry (Q2033055)

The authors study the behavior of the BFK-gluing formula [\textit{D. Burghelea} et al., J. Funct. Anal. 107, No. 1, 34--65 (1992; Zbl 0759.58043)] under conformal transformations. They prove a scaling invariance property for one of the terms of the BFK-gluing formula. This implies that the value of the zeta function at zero of the Dirichlet-to-Neumann operator can be decomposed in a function of the value at zero of the zeta function of the manifolds involved in the gluing. To conclude, the authors present all the coefficients in the BFK-gluing formula in dimension three.