Abstract

Abstract Let M be a compact hyperbolic 2-orbifold (not necessarily connected). We show that the spectrum of the Laplacian on functions on M determines the following: the volume; the total length of the mirror boundary; the number (properly counted) of conepoints of each order; and the number (properly counted) of primitive closed geodesics of each length and orientability class. This means that Laplaceisospectral hyperbolic 2-orbifolds are representation-equivalent, and hence strongly isospectral. Statement Let M be a compact hyperbolic 2-orbifold (not necessarily connected). Denote the eigenvalues of the Laplacian acting on functions on M by (Note that we don't necessarily have 0 < λ 1 because we aren't assuming that M is connected.) We call the sequence (λ 0 , λ 1 , . . .) the Laplace spectrum of * Dartmouth College. † FaMAF-CIEM, Univ. Nac. Córdoba. ‡ The authors hereby waive all copyright and related or neighboring rights to this work, and dedicate it to the public domain. This applies worldwide.