Geometric properties of eigenfunctions

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Geometrical Structure of Laplacian Eigenfunctions (2012, background): “…investigated in various mathematical and physical disciplines, including spectral theory, probability and stochastic processes, dynamical systems and quantum billiards, condensed matter physics and quantum mechanics, theory of acoustical, optical and quantum waveguides, computer sciences, etc.”
The Calderón problem in transversally anisotropic geometries (2013, background): “These topics have a large literature, and we refer to [17], [45], [46] for surveys.”
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation (2009, background): “Lower and upper bounds of the length of the nodal lines have been studied in differential geometry [18,29,37].”
Between classical and quantum (2005, methodology): “Through its creation of the Hilbert space formalism of quantum mechanics, von Neumann’s book (1932) can be seen as a mathematical implementation of Heisenberg’s idea of Umdeutung.”