2 problems

Let $S^2$ be the unit round sphere, and let $\gamma$ be a smooth Jordan curve in $S^2$. Its diameter is the supremum of the round distances between points of $\gamma$; assume that…

Let $n\ge 3$, and let a flexible polyhedron lie either in Lobachevsky space $\Lambda^n$ or in the open hemisphere $S^n_+$. Its generalized oriented volume is defined in the relevan…