On common zeros of eigenfunctions of the Laplace operator

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.

third version, new exposition, one example abolished, one reference added and one removed

Cited by in corpus (1)

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