Flexibly deformable holding elements operate such that substrates can be held in a fixed manner at a surface of the holding element electrostatically or also by use of negative pressure and planar positional deviations or unwanted deformations can be compensated simply and reliably, where at least one cut-out having an opening arranged at the rear side is formed at the rear side of the holding element which is disposed opposite the surface, and an actuator is arranged there exerting compressive forces or pulling forces for a widening or narrowing of the cut-out and/or for a deformation of the holding element.