There exists a three-dimensional standard solution to the Ricci flow: a complete rotationally symmetric Ricci flow $(\mathbb{R}^3, g(t))_{0 \leq t < 1}$ with initial metric obtained by smoothly gluing a positively curved cap to a round half-cylinder, normalized so that the cylindrical scale becomes singular at time $t = 1$.
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For every $t \in (0,1)$, the curvature operator of $g(t)$ is positive. Moreover, for every $T \in [0,1)$ and every integer $m \geq 0$, there exists a constant $C_{m,T} < \infty$ such that
for all $t \in [0,T]$, where $\operatorname{Rm}_{g(t)}$ denotes the Riemann curvature tensor of $g(t)$ and $\nabla^m \operatorname{Rm}_{g(t)}$ denotes its $m$-th covariant derivative with respect to $g(t)$.