Large solutions for biharmonic maps in four dimensions

We seek critical points of the Hessian energy functional , where or Ω is the unit disk in and u : Ω → S ⁴. We show that has a critical point which is not homotopic to the constant map. Moreover, we prove that, for certain prescribed boundary data on ∂B, E _B achieves its infimum in at least two distinct homotopy classes of maps from B into S ⁴. The author was partially supported by SNF 200021-101930/1.