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.
Nonlinear models in 2+εdimensions.Physical Review Letters, 45(13):1057
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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.