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

Bobo Hua; Yang Shen

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arXiv · 2412.21008

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

Bobo Hua·Yang Shen

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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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Bobo Hua, Yang Shen. 2024-12-30. Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary. https://arxiv.org/abs/2412.21008

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