The inner radius of nodal domains in high dimensions

Fuente: arXiv
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Autori principali: Charron, Philippe, Mangoubi, Dan
Natura: Preprint
Pubblicazione: 2023
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author Charron, Philippe
Mangoubi, Dan
author_facet Charron, Philippe
Mangoubi, Dan
contents We prove that every nodal domain of an eigenfunction of the Laplacian of eigenvalue $λ$ on a $d$-dimensional closed Riemannian manifold contains a ball of radius $cλ^{-1/2}(\logλ)^{-(d-2)/2}$. This ball is centered at a point at which the eigenfunction attains its maximum in absolute value within the nodal domain.
format Preprint
id arxiv_https___arxiv_org_abs_2306_00159
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle The inner radius of nodal domains in high dimensions
Charron, Philippe
Mangoubi, Dan
Analysis of PDEs
Differential Geometry
Spectral Theory
We prove that every nodal domain of an eigenfunction of the Laplacian of eigenvalue $λ$ on a $d$-dimensional closed Riemannian manifold contains a ball of radius $cλ^{-1/2}(\logλ)^{-(d-2)/2}$. This ball is centered at a point at which the eigenfunction attains its maximum in absolute value within the nodal domain.
title The inner radius of nodal domains in high dimensions
topic Analysis of PDEs
Differential Geometry
Spectral Theory
url https://arxiv.org/abs/2306.00159