Laplace operators with eigenfunctions whose nodal set is a knot

We prove that, given any knot γ in a compact 3-manifold M, there exists a Riemannian metric on M such that there is a complex-valued eigenfunction u of the Laplacian, corresponding to the first nontrivial eigenvalue, whose nodal set u−1(0) has a connected component given by γ. Higher dimensional analogs of this result will also be considered.