#### Vol. 314, No. 2, 2021

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Ricci flow with bounded curvature integrals

### Shota Hamanaka

Vol. 314 (2021), No. 2, 283–309
##### Abstract

We study the Ricci flow on a closed manifold and finite time interval $\left[0,T\right)$ $\left(T<\infty \right)$ 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 $T$ by an orbifold Ricci flow.

##### Keywords
Ricci flow, orbifold Ricci flow, Gromov–Hausdorff convergence
Primary: 53E20