\begin{align*}
r: M &\to [0,\infty) \\
x &\mapsto d_g(p,x)
\end{align*}
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be the distance function from $p$, and let $\mathcal{R}_p \subset M \setminus \{p\}$ denote the [open set](/page/Open%20Set) on which $r$ is smooth. Define
Equivalently, along every radial minimizing geodesic segment from $p$ whose regular points meet $U$, the radial Ricci curvature at those points equals $(n-1)k$.