Abstract:
Sharp estimates are obtained for the convex hulls of polygonal lines which are convex in $\mathbf R^n$ (i.e. which are cut by an arbitrary hyperplane no more than $n$ times) and have segments of given length and number. The extremal polygonal lines are found.
Closed and open polygonal lines are considered. Passing to the limit yields the solution of similar problems for convex curves.
Bibliography: 13 titles.
Fulltext:
PDF file (1796 kB)
