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 , 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 -dimensional compact smooth Riemannian manifold, we estimate the relation between supremum and infimum of an eigenfunction of the Laplace operator.
@article{AIF_1991__41_1_259_0,
author = {Nadirashvili, Nikolai S.},
title = {Metric properties of eigenfunctions of the Laplace operator on manifolds},
journal = {Annales de l'Institut Fourier},
volume = {41},
year = {1991},
pages = {259-265},
doi = {10.5802/aif.1256},
mrnumber = {92g:58130},
zbl = {0726.58050},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1991__41_1_259_0}
}
Nadirashvili, Nikolai S. Metric properties of eigenfunctions of the Laplace operator on manifolds. Annales de l'Institut Fourier, Tome 41 (1991) pp. 259-265. doi : 10.5802/aif.1256. http://gdmltest.u-ga.fr/item/AIF_1991__41_1_259_0/
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