  Numerous elliptic and parabolic variational problems arising in physics and
geometry (Ginzburg-Landau equations, harmonic maps, Yang-Mills fields,
Omega-instantons, Yamabe equations, geometric flows in general...) possess a
critical dimension in which an invariance group (similitudes, conformal groups)
acts. This common feature generates, in all these different situations, the
same non-linear effect. One observes a strict splitting in space between an
almost linear regime and a dominantly non-linear regime which has two major
characteristics : it requires a quantized amount of energy and arises along
rectifiable objects of special geometric interest (geodesics, minimal surfaces,
J-holomorphic curves, special Lagrangian manifolds, mean-curvature flows...).
