Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces
Ambrosio L, Erbar M, Savaré G (2016)
Nonlinear Anal. 137: 77-134.
Zeitschriftenaufsatz | Englisch
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Autor*in
Ambrosio, Luigi;
Erbar, MatthiasUniBi;
Savaré, Giuseppe
Einrichtung
Abstract / Bemerkung
We introduce the setting of extended metric-topological measure spaces as a general "Wiener-like" framework for optimal transport problems and nonsmooth metric analysis in infinite dimension.
After a brief review of optimal transport tools for general Radon measures, we discuss the notions of the Cheeger energy, of the Radon measures concentrated on absolutely continuous curves, and of the induced "dynamic transport distances." We study their main properties and their links with the theory of Dirichlet forms and the Bakry-Émery curvature condition, in particular concerning the contractivity properties and the EVI formulation of the induced Heat semigroup.
Erscheinungsjahr
2016
Zeitschriftentitel
Nonlinear Anal.
Band
137
Seite(n)
77-134
ISSN
0362-546X,1873-5215
Page URI
https://pub.uni-bielefeld.de/record/2980846
Zitieren
Ambrosio L, Erbar M, Savaré G. Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces. Nonlinear Anal. 2016;137:77-134.
Ambrosio, L., Erbar, M., & Savaré, G. (2016). Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces. Nonlinear Anal., 137, 77-134. https://doi.org/10.1016/j.na.2015.12.006
Ambrosio, Luigi, Erbar, Matthias, and Savaré, Giuseppe. 2016. “Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces”. Nonlinear Anal. 137: 77-134.
Ambrosio, L., Erbar, M., and Savaré, G. (2016). Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces. Nonlinear Anal. 137, 77-134.
Ambrosio, L., Erbar, M., & Savaré, G., 2016. Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces. Nonlinear Anal., 137, p 77-134.
L. Ambrosio, M. Erbar, and G. Savaré, “Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces”, Nonlinear Anal., vol. 137, 2016, pp. 77-134.
Ambrosio, L., Erbar, M., Savaré, G.: Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces. Nonlinear Anal. 137, 77-134 (2016).
Ambrosio, Luigi, Erbar, Matthias, and Savaré, Giuseppe. “Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces”. Nonlinear Anal. 137 (2016): 77-134.
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