ON THE ERDOS-MORDELL INEQUALITY FOR NORMED PLANES AND SPACES

In the Euclidean plane, the Erdos-Mordell inequality indicates that the sum of distances of an interior point of a triangle T to its vertices is larger than or equal to twice the sum of distances to the sides of T. We extend this theorem to arbitrary (normed or) Minkowski planes, and we generalize in an analogous way some other related inequalities, e.g. referring to polygons. We also derive Minkowskian analogues of Erdos-Mordell in-equalities for tetrahedra and n-dimensional simplices. Finally, some related inequalities are obtained which additionally involve total edge-lengths of simplices.