The boundary of rank-one divisible convex sets

TL;DR

This paper proves that for certain convex sets in projective space, the proximal limit set coincides with the entire boundary, revealing a fundamental geometric property of these structures.

Contribution

It establishes that non-symmetric irreducible divisible convex sets have a full projective boundary as their proximal limit set, a new geometric insight.

Findings

Proximal limit set equals the full boundary for these convex sets

The result applies specifically to non-symmetric irreducible divisible convex sets

Provides a deeper understanding of the boundary structure in projective convex geometry

Abstract

We prove that for any non-symmetric irreducible divisible convex set, the proximal limit set is the full projective boundary.