An implant with an open-worked, hollow cylindrical main structure composed of a multiplicity of crosspieces, wherein the implant adopts a compressed state and an expanded state. So as to achieve a greater level of radial rigidity and an increased collapse pressure in the expanded state compared to conventional implants, wherein the deliverability is not adversely affected at the same time, the density of the crosspieces in the expanded state is greater than the density of the crosspieces in the compressed state, at least in one portion of the implant. The invention further provides a system including a catheter with a balloon and an implant of the type disclosed above.