  The theorem of Chekhanov asserts that a Lagrangian submanifold L has positive
displacement energy under natural assumptions on the symplectic topology at
infinity. It is greater than or equal to the minimal area of holomorphic disks
bounded by L. This estimate was obtained by Y.V. Chekhanov in 1998. Section 1
presents a direct proof based on the use of holomorphic curves and their
Hamiltonian perturbations. In section 2, we define a filtered version of the
Lagrangian Floer homology, without any assumption on L. This is compared with
the Morse homology groups, via the continuation maps (subsubsection 2.3.2) or
the PSS maps (subsection 3.2).
