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Mat. Sb. (N.S.), 1987, Volume 133(175), Number 2(6), Pages 223–237 (Mi msb2554)  

This article is cited in 17 scientific papers (total in 17 papers)

Multiple eigenvalues of the Laplace operator

N. S. Nadirashvili


Abstract: Upper bounds are obtained for the multiplicities of the eigenvalues of the Laplace operator in a domain and on a manifold.
Bibliography: 17 titles.

Full text: PDF file (966 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1988, 61:1, 225–238

Bibliographic databases:

UDC: 517.9
MSC: 35J05, 35P15
Received: 06.05.1985 and 15.07.1986

Citation: N. S. Nadirashvili, “Multiple eigenvalues of the Laplace operator”, Mat. Sb. (N.S.), 133(175):2(6) (1987), 223–237; Math. USSR-Sb., 61:1 (1988), 225–238

Citation in format AMSBIB
\Bibitem{Nad87}
\by N.~S.~Nadirashvili
\paper Multiple eigenvalues of the Laplace operator
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 133(175)
\issue 2(6)
\pages 223--237
\mathnet{http://mi.mathnet.ru/msb2554}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=905007}
\zmath{https://zbmath.org/?q=an:0672.35049}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 61
\issue 1
\pages 225--238
\crossref{https://doi.org/10.1070/SM1988v061n01ABEH003204}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Par Colette Anné, “Fonctions Properes Sur Des Variétés Avec Des Anses Fines, Applcation À La Multiplicité”, Communications in Partial Differential Equations, 15:11 (1990), 1617  crossref  mathscinet
    2. Nikolai Nadirashvili, “Berger's isoperimetric problem and minimal immersions of surfaces”, GAFA Geom funct anal, 6:5 (1996), 877  crossref  mathscinet
    3. Rainer Hempel, Thomas Kriecherbauer, Peter Plankensteiner, “Discrete and Cantor Spectrum for Neumann Laplacians of Combs”, Math Nachr, 188:1 (1997), 141  crossref  mathscinet  zmath  isi
    4. N. Nadirashvili, “Harmonic functions with bounded number of nodal domains”, Applicable Analysis, 71:1-4 (1998), 187  crossref  mathscinet
    5. Rodrigo Banuelos, Krzysztof Burdzy, “On the “Hot Spots” Conjecture of J. Rauch”, Journal of Functional Analysis, 164:1 (1999), 1  crossref  mathscinet  zmath
    6. D. Jakobson, N. S. Nadirashvili, J. Toth, “Geometric properties of eigenfunctions”, Russian Math. Surveys, 56:6 (2001), 1085–1105  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Haskins M., “The Geometric Complexity of Special Lagrangian T-2-Cones”, Invent. Math., 157:1 (2004), 11–70  crossref  mathscinet  zmath  adsnasa  isi
    8. Hirokazu Aiba, Toru Suzuki, “Nodal domain distribution for a nonintegrable two-dimensional anharmonic oscillator”, Phys Rev E, 72:6 (2005), 066214  crossref  mathscinet  isi
    9. Jakobson D., Nadirashvili N., Polterovich I., “Extremal Metric for the First Eigenvalue on a Klein Bottle”, Can. J. Math.-J. Can. Math., 58:2 (2006), 381–400  crossref  mathscinet  zmath  isi
    10. Tlusty Ts., “A Relation Between the Multiplicity of the Second Eigenvalue of a Graph Laplacian, Courant's Nodal Line Theorem and the Substantial Dimension of Tight Polyhedral Surfaces”, Electron. J. Linear Algebra, 16 (2007), 315–324  crossref  mathscinet  zmath  isi
    11. D. S. Grebenkov, B.-T. Nguyen, “Geometrical Structure of Laplacian Eigenfunctions”, SIAM Rev, 55:4 (2013), 601  crossref  mathscinet  zmath
    12. A. V. Penskoi, “Extremal metrics for eigenvalues of the Laplace–Beltrami operator on surfaces”, Russian Math. Surveys, 68:6 (2013), 1073–1130  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. Pierre Jammes, “Prescription du spectre de Steklov dans une classe conforme”, Anal. PDE, 7:3 (2014), 529  crossref  mathscinet  zmath
    14. Gerasim Kokarev, “On multiplicity bounds for Schrödinger eigenvalues on Riemannian surfaces”, Anal. PDE, 7:6 (2014), 1397  crossref  mathscinet  zmath
    15. Hassannezhad A., Kokarev G., Polterovich I., “Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound”, J. Spectr. Theory, 6:4 (2016), 807–835  crossref  mathscinet  zmath  isi  scopus
    16. Nadirashvili N.S., Penskoi A. V., “An Isoperimetric Inequality For the Second Non-Zero Eigenvalue of the Laplacian on the Projective Plane”, Geom. Funct. Anal., 28:5 (2018), 1368–1393  crossref  mathscinet  zmath  isi  scopus
    17. Alexei V. Penskoi, “Isoperimetric Inequalities for Higher Eigenvalues of the Laplace–Beltrami Operator on Surfaces”, Proc. Steklov Inst. Math., 305 (2019), 270–286  mathnet  crossref  crossref  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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