Geodesic
Optimal Transport and Generalized Ricci Flow
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove results relating the theory of optimal transport and generalized Ricci flow. We define an adapted cost functional for measures using a solution of the associated dilaton flow. This determines a formal notion of geodesics in the space of measures, and we show geodesic convexity of an associated entropy functional. Finally, we show monotonicity of the cost along the backwards heat flow, and use this to give a new proof of the monotonicity of the energy functional along generalized Ricci flow.
Keywords: generalized Ricci flow
Mots-clés : optimal transport. 
@article{SIGMA_2024_20_a2,
     author = {Eva Kopfer and Jeffrey Streets},
     title = {Optimal {Transport} and {Generalized} {Ricci} {Flow}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2024},
     volume = {20},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a2/}
}
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Eva Kopfer; Jeffrey Streets. Optimal Transport and Generalized Ricci Flow. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a2/

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