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},
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, Tome 41 (1991) no. 1, pp. 259-265. doi : 10.5802/aif.1256. http://www.numdam.org/articles/10.5802/aif.1256/
[1] , , Problèmes aux limites non homogènes et application, vol. 1, Dunod, Paris, 1968. | Zbl
[2] , , , Partial differential equations, Providence, R.I, 1974.
[3] , Uber Knoten von Eigenfunnktionen des Laplace-Beltrami Operators, Math. Z., 158 (1978), 15-21. | EuDML | Zbl
[4] , , Nodal sets of eigenfunctions on Riemannian manifolds, Invent. Math., 93 (1988), 161-183. | EuDML | MR | Zbl
[5] , , Elliptic partial differential equations of second order, Second Edition, Springer, 1983. | MR | Zbl
Cité par Sources :
