Minkowski addition of \(H\)-convex sets and related Helly-type theorems.
Based on results on \(H\)-convex sets due to \textit{V. Boltyanski} and \textit{H. Martini} [J. Comb. Theory, Ser. A 93, No. 2, 292--309 (2001; Zbl 0976.52007)] and on the Minkowski addition of convex sets due to \textit{R. Schneider} [Convex bodies: The Brunn-Minkowski theory (Cambridge University Press, Cambridge) (1993; Zbl 0798.52001)], the authors prove a sufficient condition ensuring that the Minkowski sum of \(H\)-convex sets is itself an \(H\)-convex set. From this, using the method of \textit{L. Danzer}, \textit{B. Grünbaum} and \textit{V. Klee} [Proc. Sympos. Pure Math. 7, 101--180 (1963; Zbl 0132.17401)], they establish some theorems of Helly-type for \(H\)-convex sets.
scientific article; zbMATH DE number 1975838