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arXiv · 2306.00159

The inner radius of nodal domains in high dimensions

Philippe Charron·Dan Mangoubi
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Abstract

We prove that every nodal domain of an eigenfunction of the Laplacian of eigenvalue $\lambda$ on a $d$-dimensional closed Riemannian manifold contains a ball of radius $c\lambda^{-1/2}(\log\lambda)^{-(d-2)/2}$. 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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Philippe Charron, Dan Mangoubi. 2023-05-31. The inner radius of nodal domains in high dimensions. https://arxiv.org/abs/2306.00159

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