The first Dirichlet eigenvalue and the width

Guoyi Xu

doi:10.1016/j.jfa.2024.110709

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arXiv · 2407.10027

The first Dirichlet eigenvalue and the width

Guoyi Xu

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Abstract

For a geodesic ball with non-negative Ricci curvature and mean convex boundary, it is known that the first Dirichlet eigenvalue of this geodesic ball has a sharp lower bound in term of its radius. We show a quantitative explicit inequality, which bounds the width of geodesic ball in terms of the spectral gap between the first Dirichlet eigenvalue and the corresponding sharp lower bound.

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Guoyi Xu. 2024-07-13. The first Dirichlet eigenvalue and the width. https://doi.org/10.1016/j.jfa.2024.110709

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