# A local curvature estimate for the Ricci flow

@article{Kotschwar2015ALC, title={A local curvature estimate for the Ricci flow}, author={B. Kotschwar and Ovidiu Munteanu and J. Wang}, journal={arXiv: Differential Geometry}, year={2015} }

We show that the norm of the Riemann curvature tensor of any smooth solution to the Ricci flow can be explicitly estimated in terms of its initial values on a given ball, a local uniform bound on the Ricci tensor, and the elapsed time. This provides a new, direct proof of a result of Sesum, which asserts that the curvature of a solution on a compact manifold cannot blow up while the Ricci curvature remains bounded, and extends its conclusions to the noncompact setting. We also prove that the… CONTINUE READING

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