Quantitative stability estimates bound |λ_k(Ω) - λ_k(Θ)| by C(d,k) times (λ_2(Ω) - λ_2(Θ)) to the power α = α_d/(d+1)^2 (with α=1/2 when λ_k(Ω) ≥ λ_k(Θ)), for Θ the union of two equal balls.
Minimization of the k-th eigenvalue of the Dirichlet Laplacian
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Quantitative stability control of the full spectrum of the Dirichlet Laplacian by the second eigenvalue
Quantitative stability estimates bound |λ_k(Ω) - λ_k(Θ)| by C(d,k) times (λ_2(Ω) - λ_2(Θ)) to the power α = α_d/(d+1)^2 (with α=1/2 when λ_k(Ω) ≥ λ_k(Θ)), for Θ the union of two equal balls.