naa a22 4500 510810705 CHVBK 20180411083441.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s12220-012-9295-3 doi (NATIONALLICENCE)springer-10.1007/s12220-012-9295-3 Krein Formula and S -Matrix for Euclidean Surfaces with Conical Singularities [Elektronische Daten] [Luc Hillairet, Alexey Kokotov] Using the Krein formula for the difference of the resolvents of two self-adjoint extensions of a symmetric operator with finite deficiency indices, we establish a comparison formula for ζ-regularized determinants of two self-adjoint extensions of the Laplace operator on a Euclidean surface with conical singularities (E.s.c.s.). The ratio of two determinants is expressed through the value S(0) of the S-matrix, S(λ), of the surface. We study the asymptotic behavior of the S-matrix, give an explicit expression for S(0) relating it to the Bergman projective connection on the underlying compact Riemann surface, and derive variational formulas for S(λ) with respect to coordinates on the moduli space of E.s.c.s. with trivial holonomy. Mathematica Josephina, Inc., 2012 Flat Laplacian nationallicence Determinant nationallicence Conical singularities nationallicence Complex structure nationallicence Hillairet Luc UMR CNRS 6629, Université de Nantes, 2 rue de la Houssinière, BP 92 208, 44 322, Nantes Cedex 3, France aut Kokotov Alexey Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, H3G 1M8, Montreal, Quebec, Canada aut Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1498-1529 1050-6926 23:3<1498 2013 23 12220 https://doi.org/10.1007/s12220-012-9295-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-012-9295-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hillairet Luc UMR CNRS 6629, Université de Nantes, 2 rue de la Houssinière, BP 92 208, 44 322, Nantes Cedex 3, France aut NATIONALLICENCE 700 1- Kokotov Alexey Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, H3G 1M8, Montreal, Quebec, Canada aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1498-1529 1050-6926 23:3<1498 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer