Critical points of Laplace eigenfunctions on polygons

Chris Judge; Sugata Mondal

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arXiv · 2108.10386

Critical points of Laplace eigenfunctions on polygons

Chris Judge·Sugata Mondal

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Abstract

We study the critical points of Laplace eigenfunctions on polygonal domains with a focus on the second Neumann eigenfunction. We show that if each convex quadrilaterals has no second Neumann eigenfunction with an interior critical point, then there exists a convex quadrilateral with an unstable critical point. We also show that each critical point of a second-Neumann eigenfunction on a Lip-1 polygon with no orthogonal sides is an acute vertex.

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Chris Judge, Sugata Mondal. 2021-08-23. Critical points of Laplace eigenfunctions on polygons. https://arxiv.org/abs/2108.10386

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