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Annals of Global Analysis and Geometry

, Volume 26, Issue 2, pp 201–208 | Cite as

A Note on Common Zeroes of Laplace–Beltrami Eigenfunctions

  • V. M. Gichev
Article

Abstract

Let Δuuvv= 0, where Δ isthe Laplace–Beltrami operator on a compact connected smoothmanifold M and λ > 0. If H1(M) = 0then there exists pM such that u(p)=v(p) = 0 For homogeneous M,H1(M) ≠ 0 implies the existence of a pair u,v as above that has no common zero.

nodal set Laplace–Beltrami eigenfunction irreducible representation 

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References

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    Aronszajn, N.: A unique continuation theorem for solutions of elliptic partial differential equations of second order, J. Math. Pures Appl. 36 (1957), 23–239.Google Scholar
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    Courant, R. and Hilbert, D.: Methoden der Mathematischen Physik, Verlag von Julius Springer, Berlin, 1931.Google Scholar
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    Galindo, J., de la Harpe, P. and Vust, T.: Two observations on irreducible representations of groups, J. Lie Theory 12 (2002), 53–538.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • V. M. Gichev
    • 1
  1. 1.Omsk Branch of Sobolev Institute of MathematicsOmskRussia

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