The First Eigenvalue of the Laplacian for Plane Domains

DOI10.2307/2044213zbMath0462.35071OpenAlexW4240119707MaRDI QIDQ3913185

Christopher B. Croke

Publication date: 1981

Full work available at URL: https://doi.org/10.2307/2044213

zbMATH Keywords

connectivityfirst eigenvalueLaplacianinradiusconnected plane domain

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Inequalities and extremum problems involving convexity in convex geometry (52A40) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (12)

On principal frequencies and inradius in convex sets ⋮ Brownian motion and the fundamental frequency of a drum ⋮ On the analytic systole of Riemannian surfaces of finite type ⋮ Mini-workshop: A geometric fairytale full of spectral gaps and random fruit. Abstracts from the mini-workshop held November 27 -- December 3, 2022 ⋮ An optimal lower bound in fractional spectral geometry for planar sets with topological constraints ⋮ The spectrum of the Laplacian: A geometric approach ⋮ Brownian motion and eigenvalues for the Dirichlet Laplacian ⋮ Lower bounds of Cheeger-Osserman type for the first eigenvalue of the n- dimensional fixed membrane problem ⋮ Isoperimetric constants and some lower bounds for the eigenvalues of the P-laplacian ⋮ Semiclassical bounds for spectra of biharmonic operators ⋮ On the lowest eigenvalue of the Laplacian for the intersection of two domains ⋮ Can one see the fundamental frequency of a drum?

Cites Work

• Estimate on the fundamental frequency of a drum
• A note on Hayman's theorem on the bass note of a drum
• Some bounds for principal frequency

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