On mappings that preserve Fermat-Torricelli points

Abstract

Let $\Delta$ be the set of all triple points $\{ A, B, C \}$ in $\mathbb{R}^n$ such that the largest angle of the triangle $ABC$ is less than $\frac{2\pi}{3}$ . In this paper we proved that if a mapping $f:\mathbb{R}^n \rightarrow \mathbb{R}^n$ preserves the Fermat-Torricelli points of the triangles in $\Delta$, then f is an affine transformation.