Riemannian cut point
= Riemannian cut point
{c}
{title2=$\gamma(c(v)),\quad c(v)=\sup\{t:d(p,\gamma(t))=t\}$}
For a unit-speed <geodesic> $\gamma(t)=\exp_p(tv)$, a finite cut time $c(v)$ is the last time to which its segment from $p$ minimizes <Riemannian distance>. Its endpoint is the Riemannian cut point along that geodesic. It lies in the <cut locus>; it need not be a <cut point> in the topological sense. The segment up to the cut time still minimizes by continuity of distance.