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Metric properties of eigenfunctions of the Laplace operator on manifolds. (English) Zbl 0726.58050
On a two-dimensional compact real analytic Riemannian manifold we estimate the volume of the set on which the eigenfunction of the Laplace- Beltrami operator is positive.
On an n-dimensional compact smooth Riemannian manifold, we estimate the relation between supremum and infimum of an eigenfunction of the Laplace operator.

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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