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


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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    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
  2. 2.
    Courant, R. and Hilbert, D.: Methoden der Mathematischen Physik, Verlag von Julius Springer, Berlin, 1931.Google Scholar
  3. 3.
    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

Personalised recommendations