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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

3 votes
0 answers
118 views

Helly number of closed unit balls in R^d

Does anyone know the Helly number of closed unit balls in $\mathbf{R}^d$ and a reference? This number is the smallest number $k(d)$ so that for any collection of of closed unit balls in $\mathbf{R}^d$ …
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3 votes
0 answers
28 views

Disjoint touching bodies of constant width

Let $F$ and $F_1,\ldots,F_n$ be bodies of constant width 1 in $\mathbb{R}^d$ such that $F_1,\ldots,F_n$ are pairwise disjoint and all intersect non-trivially (i.e. in at least one point) with $F$. Wha …
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