On a Maximization Problem for the Convex Hull of Connected Systems of Segments

Fixed a set of finitely many segments in $\mathbb{R}^d$ we look for a connected system of these segments whose convex hull has the greatest d-dimensional volume, solving the problem when d and d+1 segments are considered. Some remarks about the analogous maximization problem on the set of the continuous and rectifiable curves with fixed length are also proposed.