We study the Ricci flow on ${\mathbb{R}}^{n+1}$, with $n\ge 2$, starting at some complete bounded curvature rotationally symmetric metric $g_0$. We first focus on the case where $({\mathbb{R}}^{n+1},g_0)$ does not contain minimal hyperspheres; we prove that if $g_0$ is asymptotic to a cylinder, then the solution develops a Type-II singularity and converges to the Bryant soliton after scaling, while if the curvature of $g_0$ decays at infinity, then the solution is immortal. As a corollary, we prove a conjecture by Chow and Tian about Perelman's standard solutions. We then consider a class of asymptotically flat initial data $({\mathbb{R}}^{n+1},g_0)$ containing a neck and we prove that if the neck is sufficiently pinched, in a precise way, the Ricci flow encounters a Type-I singularity.

我们研究Ricci流 ${\mathbb{[R}}^{ñ+\mathrm{1个}}$，带有 $ñ\ge 2$，从某个完全有界曲率旋转对称度量开始 $G_0$。我们首先关注的情况是$（{\mathbb{[R}}^{ñ+\mathrm{1个}}，G_0）$不包含最少的超球面；我们证明$G_0$ 对圆柱渐近，则解产生II型奇点并在缩放后收敛到科比孤子，而如果 $G_0$衰减到无穷远，那么解法是不朽的。作为推论，我们证明了Chow和Tian对Perelman的标准解决方案的猜想。然后，我们考虑一类渐近平坦的初始数据$（{\mathbb{[R}}^{ñ+\mathrm{1个}}，G_0）$ 包含一个脖子，我们证明如果脖子被精确地充分捏住，则Ricci流会遇到I型奇点。