Quantitative combinatorial geometry for continuous parameters
arXiv:1603.05523
Abstract
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.
22 pages. arXiv admin note: substantial text overlap with arXiv:1503.06116