The first Steklov eigenvalue of a Riemannian manifold with boundary is, up to constant factors, equal to the isocapacitary constant Γ∂, and the same holds for the bottom of the Dirichlet-to-Neumann spectrum in the non-compact case.
Isoperimetric control of the Steklov spectrum
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Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary
The first Steklov eigenvalue of a Riemannian manifold with boundary is, up to constant factors, equal to the isocapacitary constant Γ∂, and the same holds for the bottom of the Dirichlet-to-Neumann spectrum in the non-compact case.