2023/06/02 by Grigory Ivanov, Ivanov, Grigory, Márton Naszódi +1
Mathematics · Computer Science · #Point processes and geometric inequalities #Mathematical Dynamics and Fractals #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2306.01663
Steinitz's theorem states that if the origin belongs to the interior of the convex hull of a set Q ⊂ ℝd, then there are at most 2d points Q^′ of Q whose convex hull contains the origin in the interior. Bárány, Katchalski and Pach gave a quantitative version whereby the radius of the ball contained in the convex hull of Q^′ is bounded from below. In the present note, we show that a Euclidean result of this kind implies a corresponding spherical version.