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^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

Inner radius
Nodal domains
Remez inequality

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

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KW - Nodal domains

KW - Remez inequality

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The inner radius of nodal domains in high dimensions

Abstract

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Keywords

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