Quantitative combinatorial geometry for continuous parameters
Jesús A. De Loera, Reuben N. La Haye, David Rolnick, Pablo Soberón · arXiv (Cornell University) · 2016
We prove variations of Carathéodory's, Helly's and Tverberg's theorems where the sets involved are measured according to continuous functions such as the volume or diameter. Among our results, we present continuous quantitative versions of Lovász's colorful Helly theorem, Bárány's colorful Carathéodory's theorem, and the colorful Tverberg theorem.