Some topics in spectral geometry
The Martin compactification of a plane domain
We prove that the Martin compactification of a plane domain is homeomorphic to a subset of the two-dimensional sphere.
Metric properties of eigenfunctions of the Laplace operator on manifolds
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 -dimensional compact smooth Riemannian manifold, we estimate the relation between supremum and infimum of an eigenfunction of the Laplace operator.
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