4 papers
Microlocal analysis and spectral gap for complex hyperbolic manifolds
Travis Cunningham
We prove the existence of an essential spectral gap for convex cocompact complex hyperbolic manifolds under the hypothesis that the limit set does not contain a complex circle. We…
Distribution of zeros of holomorphic functions and resonances in logarithmic regions for Schroedinger operators on Euclidean space
Travis Cunningham
Motivated by scattering theory, this paper proves general results about the distribution of zeros in logarithmic neighborhoods of the real axis for a certain class of functions hol…
Schroedinger operators with generic potentials achieve maximal resonance density
Travis Cunningham
We show that for a generic real or complex-valued compactly supported potential, the corresponding Schroedinger operator achieves maximal resonance density, in the sense that its i…
Improved fractal Weyl bounds matching improved spectral gaps for hyperbolic surfaces and open quantum maps
Travis Cunningham
We prove a new fractal Weyl upper bound for the high-energy distribution of resonances of convex co-compact hyperbolic surfaces which matches the improved spectral gap given by Fou…