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, Ricci flow with surgery on three-manifolds, preprint, arXiv: math.DG/0303109
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Gradient Ricci shrinkers satisfy topological constraints including bounded Betti numbers and a Hodge theorem via weighted L2 cohomology.
Establishes that 3D and 4D simply connected compact quasi-Einstein manifolds with boundary and constant scalar curvature are isometric to hemispheres, cylinders, or specific products.
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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Transverse Rigidity of Shrinking Sasaki-Ricci Solitons
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.