Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions

arXiv:1110.6885 · doi:10.1007/s00220-012-1554-4

Abstract

Let Ï be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set {Ï=0}.

7 pages