A variational approach to S1-harmonic maps and applications

Abstract

We present a renormalization procedure for the Dirichlet Lagrangian for maps from surfaces with or without boundary into S1, whose finite energy critical points are the S1-harmonic maps with isolated singularities. We give some applications of this renormalization scheme in two different frameworks. The first application has to do with the renormalization of the Willmore energy for Lagrangian singular immersions into Kähler-Einstein surfaces while the second application is dealing with frame energies for surfaces immersions into Euclidian spaces.