P. Soberón

activity

20102026

most citedBalanced Convex Partitions of Measures in

R^{d}

18 citations · 41 across the 13 of their papers we have counts for

collaborators

Showing 2015Show all

3 papers · 1 filter

math.MG2015

Helly-type theorems for the diameter

Pablo Soberón

We study versions of Helly's theorem that guarantee that the intersection of a family of convex sets in $R^{d}$ has a large diameter. This includes colourful, fractional and $(p, q)$ …

math.MG2015★ 1 cited

Positive-fraction intersection results and variations of weak epsilon-nets

Alexander Magazinov, Pablo Soberón

Given a finite set $X$ of points in $R^{n}$ and a family $F$ of sets generated by the pairs of points of $X$ , we determine volumetric and structural conditions for the sets that allo…

math.MG2015★ 9 cited

Quantitative $(p, q)$ theorems in combinatorial geometry

David Rolnick, Pablo Soberón

We show quantitative versions of classic results in discrete geometry, where the size of a convex set is determined by some non-negative function. We give versions of this kind for…

Helly-type theorems for the diameter

Positive-fraction intersection results and variations of weak epsilon-nets

Quantitative (p,q) theorems in combinatorial geometry

Quantitative $(p, q)$ theorems in combinatorial geometry