Questions tagged [convex-hulls]

Let $X$ be complete $\mathop{CAT}(0)$-space and $K\subset X$ be a compact subset. Is it true that convex hull of $K$ is compact? Comments: Convex hull of $K$ = intersection of all closed convex sets ...

Given points $u, v_1, \dots,v_n \in \mathbb{R}^m$, decide if $u$ is contained in the convex hull of $v_1, \dots, v_n$. This can be done efficiently by linear programming (time polynomial in $n,m$) in ...

Does there exist a finite set of points on the Euclidean plane, such that: No 3 points are collinear, and Every one of the points has (at least) three other points in the set at the same distance ...

I am trying to understand the proof of Lemma 4.1.2 in Michel Talagrand's publication from 1995 on concentration inequalities (see below for the precise question statement): A bit of context: ...