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We give an example of a class of metrics on Sn+1 that evolve under the Ricci Flow into a “neckpinch.” We show that the solution has a Type I singularity, and that the length of the neck, i.e. the region where |Rm| ∼ (T−t)−1, is bounded from below by c √ (T − t)| log(T − t)| for some c > 0.

An example of neckpinching for Ricci flow on $S^{n+1}$