Skip to content

On the existence of Hamiltonian paths connecting Lagrangian submanifolds

Nassif Ghoussoub, Abbas Moameni

math.AParXiv:math/0508356

Abstract

We use a new variational method --based on the theory of anti-selfdual Lagrangians developed in [2] and [3]-- to establish the existence of solutions of convex Hamiltonian systems that connect two given Lagrangian submanifolds in 2N. We also consider the case where the Hamiltonian is only semi-convex. A variational principle is also used to establish existence for the corresponding Cauchy problem. The case of periodic solutions will be considered in a forthcoming paper [5].

Create a lesson