(Non-)displaceability of fibers of integrable systems has been an important
problem in symplectic geometry. In this paper, for a large class of classical
Liouville integrable systems containing the Lagrangian top, the Kovalevskaya
top and the C. Neumann problem, we find a non-displaceable fiber for each of
them. Moreover, we show that the non-displaceable fiber which we detect is the
unique fiber which is non-displaceable from the zero-section. As a special case
of this result, we also show that a singular level set of a convex Hamiltonian
is non-displaceable from the zero-section. To prove these results, we use the
notion of superheaviness introduced by Entov and Polterovich.Comment: 21 pages; some notations in Section 4 change
