  We prove that mutation of cluster-tilting objects in triangulated
2-Calabi-Yau categories is closely connected with mutation of quivers with
potentials. This gives a close connection between 2-CY-tilted algebras and
Jacobian algebras associated with quivers with potentials.
  We show that cluster-tilted algebras are Jacobian and also that they are
determined by their quivers. There are similar results when dealing with
tilting modules over 3-CY algebras. The nearly Morita equivalence for
2-CY-tilted algebras is shown to hold for the finite length modules over
Jacobian algebras.
