Two new universal inequalities for Neumann eigenvalues of the Laplacian on a planar convex domain

2025/11/22 by Funano, Kei
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2511.18043

Abstract

We establish two new universal inequalities for Neumann eigenvalues of the Laplacian on a planar convex domain.

Citations

• Geometric inequalities between Dirichlet and Neumann eigenvalues
• A universal inequality for Neumann eigenvalues of the Laplacian on a convex domain in Euclidean space
• A note on domain monotonicity for the Neumann eigenvalues of the Laplacian
• An optimal dimension-free upper bound for eigenvalue ratios
• On the role of Convexity in Isoperimetry, Spectral-Gap and Concentration
• An optimal Poincaré inequality for convex domains

Related

• A universal inequality for Neumann eigenvalues of the Laplacian on a convex domain in Euclidean space
• Inequalities between Neumann and Dirichlet Laplacian eigenvalues on planar domains
• A note on domain monotonicity for the Neumann eigenvalues of the Laplacian
• Applications of the `Ham Sandwich Theorem' to eigenvalues of the\n Laplacian
• The first Neumann eigenvalue and the width