On the lower bound of the inner radius of nodal domains

DOI10.1007/s12220-018-0050-2zbMath1428.35253arXiv1607.03816OpenAlexW2963100719MaRDI QIDQ2421231

Bogdan Georgiev

Publication date: 14 June 2019

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.03816

zbMATH Keywords

inner radiusnodal domainsLaplace eigenfunctionsconcentration of eigenfunctions

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Elliptic equations on manifolds, general theory (58J05)

Related Items (5)

Some applications of heat flow to Laplace eigenfunctions ⋮ Nodal sets of Laplace eigenfunctions under small perturbations ⋮ Some remarks on nodal geometry in the smooth setting ⋮ On maximizing the fundamental frequency of the complement of an obstacle ⋮ Density of zero sets for sums of eigenfunctions

Cites Work

• Lower bounds for nodal sets of eigenfunctions
• On the lowest eigenvalue of the Laplacian for the intersection of two domains
• \(L^{p}\) norms, nodal sets, and quantum ergodicity
• Nodal sets of eigenfunctions on Riemannian manifolds
• Applications of small-scale quantum ergodicity in nodal sets
• Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture
• Nodal geometry, heat diffusion and Brownian motion
• Can one see the fundamental frequency of a drum?
• Tubular neighborhoods of nodal sets and diophantine approximation
• On the Inner Radius of a Nodal Domain
• Local Asymmetry and the Inner Radius of Nodal Domains
• Local and global analysis of eigenfunctions
• Inner radius of nodal domains of quantum ergodic eigenfunctions

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