A Proof of the Eigenvalue Ratio Bound for Embedded Surfaces

Ricardo Gloria-Picazzo, Yingying Wu, Shing-Tung Yau

We explain how the spectrum of a closed embedded surface $\hat{I}\pounds \subset {\mathbb{R}}^3$ relates to the Dirichlet spectrum of the bounded domain $\hat{I}\text{c◯}\subset {\mathbb{R}}^3$ with $\partial Ω…