2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71034Let X be a 2-dimensional normed space, and let BX be the unit ball in X. We discuss the question of how large the set of extremal points of BX must be if X contains a well-distributed set whose distance set Delta satisfies the estimate |Δ\cap[0,N]|<CN^{3/2 -ε}. We also give a necessary and sufficient condition for the existence of a well-distributed set with |Δ\cap [0,N]| < CN.18 pagesCombinatoricsMetric Geometry52C10, 11B75text