Abstract
The Wasserstein space \(\mathcal{P}(M)\) on an Euclidean or Riemannian space M – i.e. the space of probability measures on M equipped with the L 2-Wasserstein distance d W – offers a rich geometric structure. This allows to develop a far reaching first order calculus, with striking applications for instance to the reformulation of conservative PDEs on M as gradient flows of suitable functionals on \(\mathcal{P}(M)\), see e.g. [1, 7, 11].
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Sturm, KT. (2014). A Monotone Approximation to the Wasserstein Diffusion. In: Griebel, M. (eds) Singular Phenomena and Scaling in Mathematical Models. Springer, Cham. https://doi.org/10.1007/978-3-319-00786-1_2
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