Geodesic
Inscribed balls and their centers
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12, pp. 1946-1954 Cet article a éte moissonné depuis la source Math-Net.Ru

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A ball of maximal radius inscribed in a convex closed bounded set with a nonempty interior is considered in the class of uniformly convex Banach spaces. It is shown that, under certain conditions, the centers of inscribed balls form a uniformly continuous (as a set function) set-valued mapping in the Hausdorff metric. In a finite-dimensional space of dimension $n$, the set of centers of balls inscribed in polyhedra with a fixed collection of normals satisfies the Lipschitz condition with respect to sets in the Hausdorff metric. A Lipschitz continuous single-valued selector of the set of centers of balls inscribed in such polyhedra can be found by solving $n+1$ linear programming problems. 
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M. V. Balashov. Inscribed balls and their centers. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12, pp. 1946-1954. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_12_a1/

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