2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125415In this paper, two lower bounds on the diameters of the boundary slope sets are given for Montesinos knots. One is described in terms of the minimal crossing numbers of the knots, and the other is related to the Euler characteristics of essential surfaces with the maximal/minimal boundary slopes.24 pages, 6 figuresGeometric Topology57M25text