Geodesic
Geometric properties of eigenfunctions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 56 (2001) no. 6, pp. 1085-1105

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We give an overview of some new and old results on geometric properties of eigenfunctions of Laplacians on Riemannian manifolds. We discuss properties of nodal sets and critical points, the number of nodal domains, and asymptotic properties of eigenfunctions in the high-energy limit (such as weak * limits, the rate of growth of $L^p$ norms, and relationships between positive and negative parts of eigenfunctions). 
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     author = {D. Jakobson and N. S. Nadirashvili and J. Toth},
     title = {Geometric properties of eigenfunctions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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D. Jakobson; N. S. Nadirashvili; J. Toth. Geometric properties of eigenfunctions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 56 (2001) no. 6, pp. 1085-1105. http://geodesic.mathdoc.fr/item/RM_2001_56_6_a1/