Geodesic
Best Approximations of Convex Compact Sets by Balls in the Hausdorff Metric
Matematičeskie zametki, Tome 76 (2004) no. 2, pp. 226-236

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We deduce an upper bound for the Hausdorff distance between a nonempty bounded set and the set of all closed balls in a strictly convex straight geodesic space $X$ of nonnegative curvature. We prove that the set $\chi[M]$ of centers of closed balls approximating a convex compact set in the Hausdorff metric in the best possible way is nonempty $X[M]$ and is contained in $M$. Some other properties of $\chi[M]$ also are investigated. 
@article{MZM_2004_76_2_a6,
     author = {E. N. Sosov},
     title = {Best {Approximations} of {Convex} {Compact} {Sets} by {Balls} in the {Hausdorff} {Metric}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {226--236},
     publisher = {mathdoc},
     volume = {76},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_2_a6/}
}
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E. N. Sosov. Best Approximations of Convex Compact Sets by Balls in the Hausdorff Metric. Matematičeskie zametki, Tome 76 (2004) no. 2, pp. 226-236. http://geodesic.mathdoc.fr/item/MZM_2004_76_2_a6/