A construction of conformal-harmonic maps

Olivier Biquard (1, 2) , Farid Madani (3)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 IMJ - Institut de Mathématiques de Jussieu

Conformal harmonic maps from a 4-dimensional conformal manifold to a Riemannian manifold are maps satisfying a certain conformally invariant fourth order equation. We prove a general existence result for conformal harmonic maps, analogous to the Eells–Sampson theorem for harmonic maps. The proof uses a geometric flow and relies on results of Gursky–Viaclovsky and Lamm.

Domaines: Géométrie différentielle [math.DG]

Olivier Biquard, Farid Madani. A construction of conformal-harmonic maps. Comptes Rendus. Mathématique, 2012, 350 (21-22), pp.967-970. ⟨10.1016/j.crma.2012.10.021⟩. ⟨hal-02928851⟩