The nodal set of a real function 
is its zero set,
 |
For a nonzero eigenfunction of the positive Laplace-Beltrami
operator 
on a closed Riemannian manifold with positive eigenvalue, its nodal set separates regions of opposite
sign. Its size is measured by Hausdorff measure
of dimension one less than the manifold dimension. For example, 
on the unit circle has
zeros for a positive
integer 
.
The relation between nodal size and eigenvalue is
the subject of the Yau nodal set conjecture.
