Abstract
This chapter is devoted to the following theme: Consider a family of geodesic spaces Xkich converges to some geodesic space X; does this imply that certain basic objects in the theory of optimal transport on Xk “pass to the limit”? In this chapter I shall show that the answer is affirmative: One of the main results is that the Wasserstein space P2(Xk) converges, in (local) Gromov—Hausdorff sense, to the Wasserstein space P2(X). Then I shall consider the stability of dynamical optimal transference plans, and related objects (displacement interpolation, kinetic energy, etc.). Compact spaces will be considered first, and will be the basis for the subsequent treatment of noncompact spaces.
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© 2009 Springer-Verlag Berlin Heidelberg
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Villani, C. (2009). Stability of optimal transport. In: Optimal Transport. Grundlehren der mathematischen Wissenschaften, vol 338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71050-9_28
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DOI: https://doi.org/10.1007/978-3-540-71050-9_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71049-3
Online ISBN: 978-3-540-71050-9
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