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# Mathematical Research Letters

## Volume 22 (2015)

### Number 1

### Non-trapping surfaces of revolution with long-living resonances

Pages: 23 – 42

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n1.a3

#### Authors

#### Abstract

We study resonances of surfaces of revolution obtained by removing a disk from a cone and attaching a hyperbolic cusp in its place. These surfaces include ones with non-trapping geodesic flow (every maximally extended non-reflected geodesic is unbounded) and yet infinitely many long-living resonances (resonances with uniformly bounded imaginary part, i.e., decay rate).