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

2024/12/30 by Bobo Hua, Yang Shen, Hua, Bobo +1
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2412.21008

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.

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