ИСТИНА

Spectral Geometry studies relationship between geometry of domains in an euclidean space or Riemannian manifolds and the spectrum of the Laplace operator on them. Classical questions of Spectral Geometry are well-known, among them one could mention "Can one hear the shape of a drum?" and "A drumhead of which shape produces the lowest possible sound among all drumheads of given area?” Natural problems of Spectral Geometry are very deep and their solution requires using Geometry, Topology, Analisys and Mathematical Physics including symmetry reduction.