Unique asymptotics of compact ancient solutions to three-dimensional Ricci flow. (English) Zbl 1506.53101
A solution to a geometric evolution equation is called ancient if it exists for all \( t\in (-\infty, T]\) for some \(T\). They play a central role in Perelman’s work about the singularity formation in the Ricci flow. In this paper, the authors consider compact ancient solutions to the three-dimensional Ricci flow that are \(\kappa\)-non-collapsed. They prove that such solutions either form a family of shrinking round spheres or have a unique asymptotic behavior as \(t \rightarrow -\infty\), which is described in detail by the authors. This analysis applies in particular to the ancient solution constructed by G. Perelman [arXiv e-print service 2002, Paper No. 0211159, 39 p. (2002; Zbl 1130.53001)].
Reviewer: Vincenzo Vespri (Firenze)
Citations:
Zbl 1130.53001References:
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