In continuum physics dislocations are the cause of plastic behaviour of metals.But mathematically they may be thought of as almost two codimensional concentrations of the curl of a matrix field. If the energy of the field is proportional to the square distance to ,then we are able to show a sharp lower energy bound depending on dislocation density in the framework of the geometric rigidity bounds of Friesecke,James, Mueller and others. One (and the main ) consequence is that low energy configurations are close to piecewise constant functions with values in . Most of the results are (ongoing) joint work with Gianluca Lauteri.
