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arXiv · 1605.07397

On common zeros of eigenfunctions of the Laplace operator

Dmitri Akhiezer·Boris Kazarnovskii
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Abstract

We consider the eigenfunctions of the Laplace operator $\Delta $ on a compact Riemannian manifold of dimension $n$. For $M$ homogeneous with irreducible isotropy representation and for a fixed eigenvalue of $\Delta $ we find the average number of common zeros of $n$ eigenfunctions. For this we compute the volume of the image of $M$ under an equivariant immersion into a sphere.

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Dmitri Akhiezer, Boris Kazarnovskii. 2016-05-24. On common zeros of eigenfunctions of the Laplace operator. https://doi.org/10.1007/s12188-016-0138-1

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