Nearby Lagrangian conjecture
Unsolved problem in mathematics
Prove or disprove: Any closed exact Lagrangian submanifold of the cotangent bundle of a closed manifold is Hamiltonian isotopic to the zero section.
In mathematics, more specifically symplectic topology, the nearby Lagrangian conjecture, is an open mathematical problem often attributed to Vladimir Arnold. It states that every closed exact Lagrangian submanifold of a cotangent bundle T∗M (with symplectic structure) is Hamiltonian isotopic to the zero section.
It is closely related to the theory of generating functions.