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On the existence of Hamiltonian paths connecting Lagrangian submanifolds

Nassif Ghoussoub·Abbas Moameni
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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 $\R^{2N}$. 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].

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Nassif Ghoussoub, Abbas Moameni. 2005-08-18. On the existence of Hamiltonian paths connecting Lagrangian submanifolds. https://arxiv.org/abs/math/0508356

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