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• W1995536708 abstract "Let a smooth family of Riemannian metrics $g(tau)$ satisfy the backwards Ricci flow equation on a compact oriented $n$-dimensional manifold $M$. Suppose two families of normalized $n$-forms $omega(tau) ge 0$ and $tilde omega(tau) ge 0$ satisfy the forwards (in $tau$) heat equation on $M$ generated by the connection Laplacian $Delta_{g(tau)}$. If these $n$-forms represent two evolving distributions of particles over $M$, the minimum root-mean-square distance $W_2(omega(tau),tilde omega(tau),tau)$ to transport the particles of $omega(tau)$ onto those of $tilde omega(tau)$ is shown to be non-increasing as a function of $tau$, without sign conditions on the curvature of $(M,g(tau))$. Moreover, this contractivity property is shown to characterize supersolutions to the Ricci flow." @default.
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• W1995536708 date "2010-01-01" @default.
• W1995536708 modified "2023-10-18" @default.
• W1995536708 title "Ricci flow, entropy and optimal transportation" @default.
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• W1995536708 doi "https://doi.org/10.1353/ajm.0.0110" @default.
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