IV.P171 — Breathing spectrum

The breathing spectrum on T^2 with shape ratio iota_tau has discrete positive eigenvalues accumulating only at zero; the largest eigenvalue is beta_{0,pm 1} = 1/iota_tau^2 ~ 8.585 (fundamental toroidal mode), and the fundamental eigenvalue ratio beta_{0,1}/beta_{1,0} = iota_tau^{-2}.