2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110233In this work we discuss a conjecture of Viterbo relating the symplectic capacity of a convex body and its volume. The conjecture states that among all 2n-dimensional convex bodies with a given volume the euclidean ball has maximal symplectic capacity. We present a proof of this fact up to a logarithmic factor in the dimension, and many classes of bodies for which this holds up to a universal constant.22 pagesSymplectic Geometry53D05, 53C15, 46B07, 52A20, 46B20text