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.
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.
@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},
pages = {259--265},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {41},
number = {1},
year = {1991},
doi = {10.5802/aif.1256},
mrnumber = {92g:58130},
zbl = {0726.58050},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1256/}
}
TY - JOUR AU - Nadirashvili, Nikolai S. TI - Metric properties of eigenfunctions of the Laplace operator on manifolds JO - Annales de l'Institut Fourier PY - 1991 SP - 259 EP - 265 VL - 41 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1256/ DO - 10.5802/aif.1256 LA - en ID - AIF_1991__41_1_259_0 ER -
%0 Journal Article %A Nadirashvili, Nikolai S. %T Metric properties of eigenfunctions of the Laplace operator on manifolds %J Annales de l'Institut Fourier %D 1991 %P 259-265 %V 41 %N 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1256/ %R 10.5802/aif.1256 %G en %F AIF_1991__41_1_259_0
Nadirashvili, Nikolai S. Metric properties of eigenfunctions of the Laplace operator on manifolds. Annales de l'Institut Fourier, Volume 41 (1991) no. 1, pp. 259-265. doi : 10.5802/aif.1256. http://www.numdam.org/articles/10.5802/aif.1256/
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