| Affiliation: | 1.Université Paris-Est, LAMA – CNRS UMR 8050,Créteil,France;2.Institut Universitaire de France,Paris,France;3.UPMC Univ. Paris 06, UMR 7598,Paris,France;4.CNRS, UMR 7598 LJLL,Paris,France;5.Courant Institute, New York University,New York,USA |
| Abstract: | We introduce a “Coulombian renormalized energy” W which is a logarithmic type of interaction between points in the plane, computed by a “renormalization.” We prove various of its properties, such as the existence of minimizers, and show in particular, using results from number theory, that among lattice configurations the triangular lattice is the unique minimizer. Its minimization in general remains open. |
