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We summarize the properties of eigenvalues and eigenfunctions of the Laplaceoperator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundarycondition. We keep the presentation at a level accessible to scientists fromvarious disciplines ranging from mathematics to physics and computer sciences.The main focus is put onto multiple intricate relations between the shape of adomain and the geometrical structure of eigenfunctions.

Geometrical structure of Laplacian eigenfunctions