Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary

Abstract: In this paper, we study the Steklov eigenvalue of a Riemannian manifold (M, g) with smooth boundary. For compact M , we establish a Cheeger-type inequality for the first Steklov eigenvalue by the isocapacitary constant. For non-compact M , we estimate the bottom of the spectrum of the Dirichlet-to-Neumann operator by the isocapacitary constant.