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}
}
  • B. Kotschwar, Ovidiu Munteanu, J. Wang
  • Published 2015
  • Mathematics
  • arXiv: Differential Geometry
  • 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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