The branching curves and their application to the four dimensional Ricci flow

Ilias Tergiakidis

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arXiv · 1801.07315

The branching curves and their application to the four dimensional Ricci flow

Ilias Tergiakidis

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Abstract

We study the four dimensional Ricci flow with the help of local invariants. If $(M^4, g(t))$ is a solution to the Ricci flow and $x \in M^4$, we can associate to the point $x$ a one-parameter family of curves, which lie in the product of two projective lines. This allows us to reformulate the Cheeger-Gromov-Hamilton Compactness Theorem in the context of these curves. We use this result, in order to study Type I singularities in dimension four and give a characterization of the corresponding singularity models.

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Ilias Tergiakidis. 2018-01-22. The branching curves and their application to the four dimensional Ricci flow. https://arxiv.org/abs/1801.07315

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