Dual central point theorems and their generalizations

TL;DR

This paper extends classical geometric theorems like the central point and Tverberg's theorem to scenarios involving hyperplanes and affine flats, broadening their applicability in higher-dimensional geometry.

Contribution

It introduces new analogues of central point and Tverberg's theorems for hyperplanes and affine flats, generalizing existing results.

Findings

Established new geometric theorems for hyperplanes and flats

Provided conditions under which these theorems hold

Expanded the scope of classical convex geometry results

Abstract

We prove some analogues of the central point theorem and Tverberg's theorem, where instead of points, we consider hyperplanes or affine flats of given dimension.