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Abstract
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We study the Ricci flow on a closed manifold and finite time interval
on
which certain integral curvature energies are finite. We prove that in dimension four,
such flow converges to a smooth Riemannian manifold except for finitely many
orbifold singularities. We also show that in higher dimensions, the same
assertions hold for a closed Ricci flow satisfying another condition of integral
curvature bounds. Moreover, we show that such flows can be extended over
by an
orbifold Ricci flow.
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Keywords
Ricci flow, orbifold Ricci flow, Gromov–Hausdorff
convergence
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Mathematical Subject Classification
Primary: 53E20
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Milestones
Received: 28 April 2021
Revised: 17 August 2021
Accepted: 30 August 2021
Published: 10 November 2021
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