The inner radius of nodal domains in high dimensions

Philippe Charron; Dan Mangoubi

doi:10.1016/j.aim.2024.109787

The inner radius of nodal domains in high dimensions

Philippe Charron, Dan Mangoubi

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

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 [Formula presented]. This ball is centered at a point at which the eigenfunction attains its maximum in absolute value within the nodal domain.

Original language	English
Article number	109787
Journal	Advances in Mathematics
Volume	452
DOIs	https://doi.org/10.1016/j.aim.2024.109787
State	Published - Aug 2024

Keywords

Inner radius
Nodal domains
Remez inequality

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2024.109787

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title = "The inner radius of nodal domains in high dimensions",

abstract = "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 [Formula presented]. This ball is centered at a point at which the eigenfunction attains its maximum in absolute value within the nodal domain.",

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author = "Philippe Charron and Dan Mangoubi",

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year = "2024",

month = aug,

doi = "10.1016/j.aim.2024.109787",

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AU - Charron, Philippe

AU - Mangoubi, Dan

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AB - 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 [Formula presented]. This ball is centered at a point at which the eigenfunction attains its maximum in absolute value within the nodal domain.

KW - Inner radius

KW - Nodal domains

KW - Remez inequality

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U2 - 10.1016/j.aim.2024.109787

DO - 10.1016/j.aim.2024.109787

M3 - مقالة

SN - 0001-8708

VL - 452

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 109787

ER -

The inner radius of nodal domains in high dimensions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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