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The Steklov and Laplacian spectra of Riemannian manifolds with boundary
Given two compact Riemannian manifolds $M_1$ and $M_2$ such that their respective boundaries $\Sigma_1$ and $\Sigma_2$ admit neighbourhoods $\Omega_1$ and $\Omega_2$ which are isometric, we prove the existence of a constant $C$ such that $