Abstract
In each dimension N ≥ 3 and for each real number λ ≥1, we construct a family of complete rotationally symmetric solutions to Ricci flow on ℝ N , which encounter a global singularity at a finite time T. The singularity forms arbitrarily slowly with the curvature blowing up arbitrarily fast at the rate (T − t)−(λ+1). Near the origin, blow-ups of such a solution converge uniformly to the Bryant soliton. Near spatial infinity, blow-ups of such a solution converge uniformly to the shrinking cylinder soliton. As an application of this result, we prove that there exist standard solutions of Ricci flow on ℝ N whose blow-ups near the origin converge uniformly to the Bryant soliton.
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