A hyperbolic surface is a surface with geometry modeled on the hyperbolic plane. Spectral
theory in this context refers generally to the Laplacian operator induced by the hyperbolic …

Mathematical study of scattering resonances | Bulletin of Mathematical Sciences Skip to main
content SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Bulletin …

For all convex co-compact hyperbolic surfaces, we prove the existence of an essential
spectral gap, that is, a strip beyond the unitarity axis in which the Selberg zeta function has …

We obtain an essential spectral gap for n-dimensional convex co-compact hyperbolic
manifolds with the dimension δ δ of the limit set close to n-1\over 2 n-1 2. The size of the gap …

We study eigenvalues of quantum open baker's maps with trapped sets given by linear
arithmetic Cantor sets of dimensions δ ∈ (0, 1) δ∈(0, 1). We show that the size of the …

For sequences (X j) of random closed hyperbolic surfaces with volume Vol (X j) tending to
infinity, we prove that there exists a universal constant E> 0 such that for all ϵ> 0, the …

For the paradigmatic three-disk scattering system, we confirm a recent conjecture for open
chaotic systems, which claims that resonance states are composed of two factors. In …

We study the distribution of resonances for geometrically finite hyperbolic surfaces of infinite
area by counting resonances numerically. The resonances are computed as zeros of the …

arXiv:2407.21506v1 [math.SP] 31 Jul 2024 Page 1 arXiv:2407.21506v1 [math.SP] 31 Jul
2024 SPECTRAL GAP FOR RANDOM SCHOTTKY SURFACES IRVING CALDERÓN …

Abstract Let X=\varGamma\H^2 be a convex co-compact hyperbolic surface and let δ be the
Hausdorff dimension of the limit set. Let Δ X be the hyperbolic Laplacian. We show that the …