Some remarks on critical sets of Laplace eigenfunctions

2022/04/25 by Chris Judge, Judge, Chris, Sugata Mondal +1 · 1 citation
Mathematics · #58J05 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2204.11968

openalex publication_date 2022/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the set of critical points of a solution to Δu = λ⋅ u and in particular components of the critical set that have codimension 1. We show, for example, that if a second Neumann eigenfunction of a simply connected polygon P has infinitely many critical points, then P is a rectangle.

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