Coarse uniqueness of a closest point in a hyperbolic metric space
= Coarse uniqueness of a closest point in a hyperbolic metric space
If $Y$ is convex in a $\delta$-hyperbolic metric space and two points of $Y$ both minimize distance from $x$, then their distance is at most $4\delta$. Thus a closest-point projection to $Y$, when it exists, is unique up to uniformly bounded error.