Modifying the curvature in magnetic nanostructures is a novel and elegant way toward tailoring physical phenomena at the nanoscale, allowing one to overcome limitations apparent in planar counterparts. Here, we address curvature-driven changes of static magnetic properties in cylindrically curved magnetic segments with different radii of curvature. The curved architectures are prepared by capping nonmagnetic micrometer- and nanometer-sized rolled-up membranes with a soft-magnetic 20 nm thick permalloy (Ni(80)Fe(20)) film. A quantitative comparison between the magnetization reversal processes in caps with different diameters is given. The phase diagrams of magnetic equilibrium domain patterns (diameter versus length) are generated. For this, joint experimental, including X-ray magnetic circular dichroism photoelectron emission microscopy (XMCD-PEEM), and theoretical studies are carried out. The anisotropic magnetostatic interaction in cylindrically curved architectures originating from the thickness gradient reduces substantially the magnetostatic interaction between closely packed curved nanowires. This feature is beneficial for racetrack memory devices, since a much higher areal density might be achieved than possible with planar counterparts.