Metric properties of eigenfunctions of the Laplace operator on manifolds

Nikolai S. Nadirashvili

Annales de l'institut Fourier (1991)

  • Volume: 41, Issue: 1, page 259-265
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Nadirashvili, Nikolai S.. "Metric properties of eigenfunctions of the Laplace operator on manifolds." Annales de l'institut Fourier 41.1 (1991): 259-265. <http://eudml.org/doc/74916>.

@article{Nadirashvili1991,
abstract = {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.},
author = {Nadirashvili, Nikolai S.},
journal = {Annales de l'institut Fourier},
keywords = {nodal set; eigenfunction; Laplace-Beltrami operator},
language = {eng},
number = {1},
pages = {259-265},
publisher = {Association des Annales de l'Institut Fourier},
title = {Metric properties of eigenfunctions of the Laplace operator on manifolds},
url = {http://eudml.org/doc/74916},
volume = {41},
year = {1991},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 41
IS - 1
SP - 259
EP - 265
AB - 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.
LA - eng
KW - nodal set; eigenfunction; Laplace-Beltrami operator
UR - http://eudml.org/doc/74916
ER -

References

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  1. [1] J.-P. LIONS, E. MAGENES, Problèmes aux limites non homogènes et application, vol. 1, Dunod, Paris, 1968. Zbl0165.10801
  2. [2] L. BERS, F. JOHN, M. SCHECHTER, Partial differential equations, Providence, R.I, 1974. Zbl0143.32403
  3. [3] J. BRÜNING, Uber Knoten von Eigenfunnktionen des Laplace-Beltrami Operators, Math. Z., 158 (1978), 15-21. Zbl0349.58012
  4. [4] H. DONNELLY, C. FEFFERMAN, Nodal sets of eigenfunctions on Riemannian manifolds, Invent. Math., 93 (1988), 161-183. Zbl0659.58047MR89m:58207
  5. [5] D. GILBARG, N.S. TRUDINGER, Elliptic partial differential equations of second order, Second Edition, Springer, 1983. Zbl0562.35001MR86c:35035

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