On Conformal Spectral Gap Estimates of the Dirichlet-Laplacian

2018/11/20 by Vladimir Gol’dshtein, Valerii Pchelintsev, Gol'dshtein, V. +3
Computer Science · Mathematics · Physics and Astronomy · #30C65 #35P15 #46E35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1811.08285

openalex publication_date 2018/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study spectral stability estimates of the Dirichlet eigenvalues of the Laplacian in non-convex domains Ω⊂\mathbb R². With the help of these estimates we obtain asymptotically sharp inequalities of ratios of eigenvalues in the frameworks of the Payne-Pólya-Weinberger inequalities. These estimates are equivalent to spectral gap estimates of the Dirichlet eigenvalues of the Laplacian in non-convex domains in terms of conformal (hyperbolic) geometry.

Related

• Conformal spectral stability for the Dirichlet-Laplace operator
• Conformal Spectral Stability Estimates for the Neumann Laplacian
• Spectral Gap Estimates on Conformally Flat Manifolds
• Geometric inequalities between Dirichlet and Neumann eigenvalues
• Conformal composition operators with applications to Dirichlet eigenvalues