Asymptotics of the determinant of the Laplacian on hyperbolic surfaces of finite volume (Q1312806)

For compact surfaces the height (i.e., the negative logarithm of the determinant of the Laplacian) is a spectral invariant. There is a formula (due to Polyakov) relating the height of one surface to the height of any conformal equivalent surface. Another result is a theorem of Wolpert which gives the asymptotic behavior of the height on degenerating hyperbolic surfaces. The author generalizes the definition of the height and these two results to a class of noncompact admissible surfaces consisting of compact surfaces with a finite number of finite volume hyperbolic cusps glued in.