Un-reduction in field theory, with applications

Abstract

The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one independent variable (for instance, time and an additional labelling parameter). Other possibilities are also explored: non-linear $σ$-models and the hyperbolic flows of curves.

Final version, comments still welcome!