Determinants of Dirichlet and Neumann Laplacians on Constant Curvature Surfaces with Geodesic Polygonal Boundary

We express the zeta regularized determinants of the Dirichlet and Neumann Laplacians on compact Riemann surfaces with constant curvature metrics and geodesic polygonal boundary in terms of the Laplacian determinant on their closed conical doubles. The formulae apply without restrictions on the genus