A device for the lithography-based additive manufacturing of three-dimensional structures on a substrate, comprises a carrier element for carrying a substrate having a curved surface, a light engine designed for the dynamic patterning of light in an exposure field of said light engine, a material transport unit comprising a first drive means for transporting a material layer across the exposure field, second drive means for causing rotational movement of the substrate having the curved surface such as to establish a rolling contact of the curved surface on the material layer in a contact zone, said contact zone being arranged in the exposure field, and first control means configured to control said first and/or second drive means so that said rolling contact of the curved surface on the material layer is essentially slip-free.