Alcuni problemi variazionali geometrici suggeriti dalla Fisica

We deal with some variational problems with geometrical constraints of homological or homotopical type, or in fiber bundle ambients. These models arise in condensed matter Physics to describe phase transitions at low temperature (Allen-Cahn or Ginzburg-Landau models), and also in particle Physics (abelian Higgs models). We characterize the asymptotic behavior of equilibrium configurations, corresponding to global minimizers of the involved functionals, whose energy concentrate on codimension one or two minimal surfaces.