On the Hofer geometry for weakly exact Lagrangian submanifolds

Abstract

We use spectral invariants in Lagrangian Floer theory in order to show that there exist isometric embeddings of normed linear spaces (finite or infinite-dimensional, depending on the case) into the space of Hamiltonian deformations of certain weakly exact Lagrangian submanifolds in tame symplectic manifolds. In addition to providing a new class of examples in which the Lagrangian Hofer metric can be computed explicitly, we refine and generalize some known results about it.