  In the last decades, many mathematicians have studied the curl operator in
compact three-manifolds , mainly the structure of its spectrum and some
isoperimetric problems associated with it. In this paper, we will see that all
the compact three-manifolds (both closed and and with non-empty boundary) have
always optimal lower bounds for the absolute value of their non-null
eigenvalues of curl. We will also show that these bounds are always attained
and compute the optimal domains and the multiplicities of their associated
eigenvalues. So, we have solved the isoperimetric problem associated to the
curl operator, and, by the way, we have solved and old Cantarella, de Turck,
Gluck and Teytel conjecture in the negative.
