The eigenfunctions of Laplace-Beltrami operator are often used as the basis of functions defined on some manifolds. It seems that there is some kind of connection between eigen analysis of Laplace-Beltrami operator and the natural vibration analysis of objects. I wonder, is my intuition true? What is the physical meaning of Laplace-Beltrami eigenfunctions?

For now, I only know that the eigenfunctions of the Laplace-Beltrami operator are real and orthogonal, thus they could be used as the basis of functions on the manifold where the functions are defined.

  • 2
    $\begingroup$ math.stackexchange.com/questions/264480/… $\endgroup$ Dec 24 '12 at 9:17
  • $\begingroup$ Actually, I posted the same question on the two sites because I'm not sure which category fits my question more. Thanks anyway for providing help, @John Rennie. $\endgroup$
    – Fei Zhu
    Dec 24 '12 at 11:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.