no. 1
Metric properties of eigenfunctions of the Laplace operator on manifolds
Annales de l'Institut Fourier, Tome 41 (1991) no. 1, pp. 259-265.

Sur une surface riemannienne compacte analytique réelle, nous estimons l’aire du domaine sur lequel une fonction propre du laplacien est positive.

Sur une variété riemannienne compacte de dimension n, nous estimons le rapport entre le minimum et le maximum d’une fonction propre du laplacien.

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 n-dimensional compact smooth Riemannian manifold, we estimate the relation between supremum and infimum of an eigenfunction of the Laplace operator.

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     author = {Nadirashvili, Nikolai S.},
     title = {Metric properties of eigenfunctions of the {Laplace} operator on manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {259--265},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {41},
     number = {1},
     year = {1991},
     doi = {10.5802/aif.1256},
     mrnumber = {92g:58130},
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Nadirashvili, Nikolai S. Metric properties of eigenfunctions of the Laplace operator on manifolds. Annales de l'Institut Fourier, Tome 41 (1991) no. 1, pp. 259-265. doi : 10.5802/aif.1256. https://aif.centre-mersenne.org/articles/10.5802/aif.1256/

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[2] L. Bers, F. John, M. Schechter, Partial differential equations, Providence, R.I, 1974.

[3] J. Brüning, Uber Knoten von Eigenfunnktionen des Laplace-Beltrami Operators, Math. Z., 158 (1978), 15-21. | EuDML | Zbl

[4] H. Donnelly, C. Fefferman, Nodal sets of eigenfunctions on Riemannian manifolds, Invent. Math., 93 (1988), 161-183. | EuDML | MR | Zbl

[5] D. Gilbarg, N.S. Trudinger, Elliptic partial differential equations of second order, Second Edition, Springer, 1983. | MR | Zbl

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