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Ricci flow on Riemannian groupoids

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arxiv 1411.6058 v3 pith:HNLPEVHJ submitted 2014-11-22 math.DG

classification math.DG
keywords groupoidsflowricciriemannianassumebreathersclosedcompact
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On 3-manifolds with pointwise pinched nonnegative Ricci curvature

    math.DG 2019-08 conditional novelty 7.0 of 10

    A complete Riemannian 3-manifold with bounded sectional curvature, pointwise c-pinched nonnegative Ricci curvature, and sectional curvature bounded below by -A/d(m,m0)^2 is flat or compact.

  2. On the long-time behavior of immortal Ricci flows

    math.DG 2019-08 conditional novelty 6.0 of 10

    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.

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