Geometric estimation of a potential and cone conditions of a body

Stationary radial centers and symmetry of convex polytopes

“…In [21], it was shown that if h ≥ √ m + 2 diam Ω, then Ω has a unique illuminating center, and that, as h goes to infinity, the unique illuminating center converges to the centroid of Ω. In [23], it was shown that the limit point of any convergent sequence of illuminating centers c(h j ) of height h j with h j → 0 + is an r −1−m -center. Thus an illuminating center moves with respect to h in general.…”