@article {Gigli2019,
	title = {Benamou{\textendash}Brenier and duality formulas for the entropic cost on RCD*(K,N) spaces},
	journal = {Probability Theory and Related Fields},
	year = {2019},
	month = {Apr},
	abstract = {<p>In this paper we prove that, within the framework of $\textsf{RCD}^\star(K,N)$ spaces with $N\&lt;\infty$, the entropic cost (i.e. the minimal value of the Schr{\"o}dinger problem) admits:A threefold dynamical variational representation, in the spirit of the Benamou{\textendash}Brenier formula for the Wasserstein distance; A Hamilton{\textendash}Jacobi{\textendash}Bellman dual representation, in line with Bobkov{\textendash}Gentil{\textendash}Ledoux and Otto{\textendash}Villani results on the duality between Hamilton{\textendash}Jacobi and continuity equation for optimal transport;A Kantorovich-type duality formula, where the Hopf{\textendash}Lax semigroup is replaced by a suitable {\textquoteleft}entropic{\textquoteright} counterpart.We thus provide a complete and unifying picture of the equivalent variational representations of the Schr{\"o}dinger problem as well as a perfect parallelism with the analogous formulas for the Wasserstein distance. Riemannian manifolds with Ricci curvature bounded from below are a relevant class of $\textsf{RCD}^*(K,N)$ spaces and our results are new even in this setting.</p>},
	issn = {1432-2064},
	doi = {10.1007/s00440-019-00909-1},
	url = {https://doi.org/10.1007/s00440-019-00909-1},
	author = {Nicola Gigli and Luca Tamanini}
}
@article {1607.05188,
	title = {Behaviour of the reference measure on RCD spaces under charts},
	year = {2016},
	author = {Nicola Gigli and Enrico Pasqualetto}
}
