2019/12/24 by Klaus Kirsten, Kirsten, Klaus, Yoonweon Lee +1
Mathematics · Physics and Astronomy · #58J20 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #hep-th #math-ph #math.DG #math.MP #math.SP #msc:58J20
paper · pdf · doi:10.48550/arxiv.1912.11433
28 pages
arxiv created 2019/12/24 · arxiv updated 2019/12/25
In the proof of the BFK-gluing formula for zeta-determinants of Laplacians there appears a real polynomial whose constant term is an important ingredient in the gluing formula. This polynomial is determined by geometric data on an arbitrarily small collar neighborhood of a cutting hypersurface. In this paper we express the coefficients of this polynomial in terms of the scalar and principal curvatures of the cutting hypersurface embedded in the manifold when this hypersurface is 2-dimensional. Similarly, we express some coefficients of the heat trace asymptotics of the Dirichlet-to-Neumann operator in terms of the scalar and principal curvatures of the cutting hypersurface.