Differential Forms on Wasserstein Space and Infinite Dimensional Hamiltonian Systems is popular PDF and ePub book, written by Wilfrid Gangbo in 2010, it is a fantastic choice for those who relish reading online the Differential forms genre. Let's immerse ourselves in this engaging Differential forms book by exploring the summary and details provided below. Remember, Differential Forms on Wasserstein Space and Infinite Dimensional Hamiltonian Systems can be Read Online from any device for your convenience.
Differential Forms on Wasserstein Space and Infinite Dimensional Hamiltonian Systems Book PDF Summary
Let $\mathcal{M}$ denote the space of probability measures on $\mathbb{R}^D$ endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely continuous curves in $\mathcal{M}$ was introduced by Ambrosio, Gigli, and Savare. In this paper the authors develop a calculus for the corresponding class of differential forms on $\mathcal{M}$. 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. 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. Throughout the paper the authors emphasize the geometric viewpoint and the role played by certain diffeomorphism groups of $\mathbb{R}^D$.
Detail Book of Differential Forms on Wasserstein Space and Infinite Dimensional Hamiltonian Systems PDF
- Author : Wilfrid Gangbo
- Release : 24 June 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821849392
- Genre : Differential forms
- Total Page : 90 pages
- Language : English
- PDF File Size : 16,5 Mb
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