The inner radius of nodal domains in high dimensions

2023/05/31 by Philippe Charron, Charron, Philippe, Dan Mangoubi +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2306.00159

openalex publication_date 2023/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Cited by

• On the nodal domain count under metric perturbations, Courant sharpness and boundary intersections

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