Published in Journal of Gökova Geometry Topology, Volume 1 (2007)
Title Locality of continuous Hamiltonian flows and Lagrangian intersections with the conormal of open subsets
Author Yong-Geun Oh
In this paper, we prove that if a continuous Hamiltonian flow fixes the points in an open subset U of a symplectic manifold (M, Ω), then its associated Hamiltonian is constant at each moment on U. As a corollary, we prove that the Hamiltonian of compactly supported continuous Hamiltonian flows is unique both on a compact M with contact-type boundary ∂M and on a non-compact manifold bounded at infinity. An essential tool for the proof of the locality is the Lagrangian intersection theorem for the conormals of open subsets proven by Kasturirangan and the author, combined with Viterbo's scheme that he introduced in the proof of uniqueness of the Hamiltonian on a closed manifold. We also prove the converse of the theorem which localizes a previously known global result in symplectic topology.
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Submitted: January 23, 2007
Revised: March 16, 2007
Accepted: March 18, 2007
 Journal of GGT Volume 1

Last updated: December 2007
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