The Yau nodal set conjecture predicts two-sided bounds of order 
for the nodal set of a nonzero real Laplace eigenfunction
with eigenvalue 
on a fixed closed connected smooth Riemannian
manifold. With 
, 
, and 
the manifold dimension,
the bounds are
 |
Here 
is Hausdorff measure, and both positive constants are independent of the eigenfunction
and eigenvalue.
