Excited resonance widths for Helmholtz resonators with straight neck (Q2192441)

Summary: We consider resonances associated with excited eigenvalues of the cavity of a general Helmholtz resonator with straight neck. Under the assumption that the neck stays away from the nodal set of the corresponding eigenstate, we generalise the optimal exponential lower bound on the width of the resonance, that we have obtained in a previous paper [the authors, Duke Math. J. 165, No. 14, 2793--2810 (2016; Zbl 1366.81167)] for the ground resonance only.