Metric properties of eigenfunctions of the Laplace operator on manifolds (Q804054)

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.