# Metric properties of eigenfunctions of the Laplace operator on manifolds

Annales de l'institut Fourier (1991)

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

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topNadirashvili, 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

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

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