with R. Hardt, Applications of Scans and Fractional Power Integrands, in Variational Problems in Riemannian Geometry, P. Baird et al. editors, Birkhauser, Progr. Nonlinear Differential Equations Appl., 59, 2004. 19-31.
In this note we describe the notion of a rectifiable scan and consider some applications to Plateau-type minimization problems. "Scans" were first considered in the work of Tristan Rivière and the second author to adequately describe certain bubbling phenomena. There, the behaviour of certain W1,3 weakly convergent sequences of smooth maps from four-dimensional domains into S2 led to the consideration of a necessarily infinite mass generalization of a rectifiable current. The definition of a scan is motivated by the fact that a rectifiable current can be expressed in terms of its lower-dimensional slices by oriented affine subspaces. By integral geometry, the slicing function for the rectifiable current is a mass integrable function of the subspaces. With a scan one considers more general such functions that are not necessarily mass integrable.