Bounded-curvature, bounded-diameter immortal Ricci flows admit only orbifold limits, and type-III flows with sub-logarithmic mu_+ entropy growth are volume non-collapsed with negative Einstein blowdown limits.
Ricci flow on Riemannian groupoids
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abstract
We study the Ricci flow on Riemannian groupoids. We assume that these groupoids are closed and that the space of orbits is compact and connected. We prove the short time existence and uniqueness of the Ricci flow on these groupoids. We also define a F-functional and derive the corresponding results for steady breathers on these spaces.
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math.DG 1years
2019 1verdicts
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On the long-time behavior of immortal Ricci flows
Bounded-curvature, bounded-diameter immortal Ricci flows admit only orbifold limits, and type-III flows with sub-logarithmic mu_+ entropy growth are volume non-collapsed with negative Einstein blowdown limits.