The paper extends Perelman's entropy functionals to 4D Lorentzian spacetimes and proves long-time well-posedness of Ricci flow using gradient flow properties of the coupled system.
On renormalization group flows in four dimensions.Journal of High Energy Physics, 2011(12):1–20, 2011
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Well-posedness of Ricci Flow in Lorentzian Spacetime and its Entropy Formula
The paper extends Perelman's entropy functionals to 4D Lorentzian spacetimes and proves long-time well-posedness of Ricci flow using gradient flow properties of the coupled system.