The nearby Lagrangian conjecture asserts that every closed exact embedded Lagrangian submanifold of the cotangent bundle 
of a closed connected smooth manifold 
is Hamiltonian isotopic to the zero
section. Here closed means compact without boundary, and exactness means that the canonical 1-form
restricts to 
on the submanifold. The isotopy is required to have compact
support in the cotangent bundle.
Nearby Lagrangian Conjecture
See also
Cotangent Bundle, Hamiltonian Isotopy, Lagrangian SubmanifoldExplore with Wolfram|Alpha
References
Abouzaid, M.; Courte, S.; Guillermou, S.; and Kragh, T. "Twisted Generating Functions and the Nearby Lagrangian Conjecture." Duke Math. J. 174, 949-1011, 2025. https://doi.org/10.1215/00127094-2024-0052.Cite this as:
Weisstein, Eric W. "Nearby Lagrangian Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NearbyLagrangianConjecture.html