Multiple eigenvalues and the width

2025/12/17 by Hu, Qixuan
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2512.15050

Abstract

We obtain the simplicity of the first Neumann eigenvalue of convex thin domain with boundary in Rⁿ and compact thin manifolds with non-negative Ricci curvature. For convex thin domain in R², we get the simplicity of the first k Neumann eigenvalues. The number k depends on the ratio of the corresponding width over the diameter of the domain. For convex thin domain in Rⁿ, we obtain the eigenvalue comparison with collapsing segment.

Citations

• The first Neumann eigenvalue and the width
• Neumann Isoperimetric Constant Estimate for Convex Domains
• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator

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