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arXiv · 2104.10300

Ricci flow with bounded curvature integrals

Shota Hamanaka
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Abstract

In this paper, we study the Ricci flow on a closed manifold and finite time interval $[0,T)~(T < \infty)$ 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 conditions of integral curvature bounds. Moreover, we show that such flows can be extended over $T$ by an orbifold Ricci flow.

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Shota Hamanaka. 2021-04-21. Ricci flow with bounded curvature integrals. https://doi.org/10.2140/pjm.2021.314.283

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