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arXiv · 1204.6733

The Long-Time Behavior of the Ricci Tensor Under The Ricci Flow

Christian Hilaire
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Abstract

We show that, given an immortal solution to the Ricci flow on a closed manifold with uniformly bounded curvature and diameter, the Ricci tensor goes to zero as t goes to infinity. We also show that if there exists an immortal solution on a closed 3-dimensional manifold such that the product of the square of the diameter with the norm of the curvature tensor is uniformly bounded, then the solution must be of type III.

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Christian Hilaire. 2012-04-30. The Long-Time Behavior of the Ricci Tensor Under The Ricci Flow. https://arxiv.org/abs/1204.6733

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