On the action of the Hamiltonian group on the space of Lagrangian submanifolds with boundary.

This research explores the action of the Hamiltonian group on the space of Lagrangian submanifolds with boundary. Understanding this action is fundamental for developing a more complete geometric framework for systems with boundaries and constraints. The paper delves into the Lie theoretic aspects of this action, examining its orbit structure and invariants. Potential applications lie in areas such as geometric mechanics, control theory for systems with boundaries, and the study of singular Lagrangian submanifolds.