We prove an optimal exponential lower bound on the width of the resonance associated to the first eigenvalue of the cavity for a general Helmholtz resonator with straight neck, in any dimension.
"Resonance widths for general Helmholtz resonators with straight neck." Duke Math. J. 165 (14) 2793 - 2810, 1 October 2016. https://doi.org/10.1215/00127094-3644795