The paper confirms the Hamilton-Tian conjecture for Sasaki-Ricci flow on compact transverse Fano quasi-regular Sasakian 5-manifolds with klt singularities, derives soliton compactness, and extends the result to general transverse Fano Sasakian 5-manifolds via the second Sasakian structure theorem.
Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint, arXiv: math.DG/0307245
4 Pith papers cite this work. Polarity classification is still indexing.
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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.
Establishes explicit bound on stable Andrews-Curtis moves for thickenable trivial-group presentations and proves the unstable conjecture holds for them.
Establishes transverse rigidity criteria for shrinking Sasaki-Ricci solitons and classifies low-dimensional constant-scalar-curvature examples as Sasaki-Einstein plus harmonic-Weyl cases as spherical quotients.
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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.