The Fermat-Torricelli problem in the projective plane - Tsakiris, Manolis C.; Xu, Sihang (MATHEMATICA SCANDINAVICA, 2022)
We pose and study the Fermat-Torricelli problem for a triangle in the projective plane under the sine distance. Our main finding is that if every side of the triangle has length greater than $\sin 60^° $, then the Fermat-Torricelli point is the vertex opposite the longest side. Our proof relies on a complete characterization of the equilateral case together with a deformation argument.