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math.DS2020
Spectral theory of the frame flow on hyperbolic 3-manifolds (with an appendix by Charles Hadfield)
Colin Guillarmou, Charles Hadfield, Benjamin Küster
We study the spectral theory and the resolvent of the vector field generating the frame flow of closed hyperbolic 3-dimensional manifolds on some family of anisotropic Sobolev spac…
math.DS2018
Zeta Function at Zero for Surfaces with Boundary
Charles Hadfield
We study the Ruelle zeta function at zero for negatively curved oriented surfaces with boundary. At zero, the zeta function has a zero and its multiplicity is shown to be determine…
math.DS2017
Ruelle and Quantum Resonances for Open Hyperbolic Manifolds
Charles Hadfield
We establish a direct classical-quantum correspondence on convex cocompact hyperbolic manifolds between the spectrums of the geodesic flow and the Laplacian acting on natural tenso…