A characterisation of Euclidean normed planes via bisectors

Javier Cabello Sánchez, Adrián Gordillo-Merino

Our main result states that whenever we have a non-Euclidean norm $\Vert \cdot \Vert$ on a two-dimensional vector space $X$, there exists some $x\ne 0$ such that for every $\lambda \ne 1,\lambda >0$,…