2 citations · 2 across the 1 of their papers we have counts for
4 papers
Selberg's zeta function and the spectral geometry of geometrically finite hyperbolic surfaces
D. Borthwick, C. Judge, P. A. Perry
For hyperbolic Riemann surfaces of finite geometry, we study Selberg's zeta function and its relation to the relative scattering phase and the resonances of the Laplacian. As an ap…
Determinants of Laplacians and Isopolar Metrics on Surfaces of Infinite Area
D. Borthwick, C. Judge, P. A. Perry
We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, t…
Tracking eigenvalues to the frontier of moduli space II: Limits for eigenvalue branches
Chris Judge
We prove the existence of limits of real-analytic Laplace eigenvalue branches for real-analytic families of metrics that degenerate along a compact hypersurface.
Tracking eigenvalues to the frontier of moduli space I: Convergence and spectral accumulation
Chris Judge
We study the limiting behavior of eigenfunctions/eigenvalues of the Laplacian of a family of Riemannian metrics that degenerates on a hypersurface. Our results generalize earlier w…