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Admin RapidRAR re-uploaded with new RAR file(s) (users who couldn't download some parts need to download all parts again). In accordance with the Digital Millennium Copyright Act of 1998 (the text of which may be found on the U.S. If you believe that your copywriten work has been copied in a way that constitutes copyright infringement, please notify Demonoid's copyright agent using the following form. A differential calculus for a certain class of absolutely continuous curves in $\mathcal{M}$ was introduced by Ambrosio, Gigli, and Savare.

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In this paper the authors develop a calculus for the corresponding class of differential forms on $\mathcal{M}$. The administrator of this site ( cannot be held responsible for what its users post, or any other actions of its users.
In particular they prove an analogue of Green's theorem for 1-forms and show that the corresponding first cohomology group, in the sense of de Rham, vanishes.

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For $D=2d$ the authors then define a symplectic distribution on $\mathcal{M}$ in terms of this calculus, thus obtaining a rigorous framework for the notion of Hamiltonian systems as introduced by Ambrosio and Gangbo.

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