On p-harmonic maps into spheres

Stability and singularities of harmonic maps into spheres

Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces

The story begins with the paper of Müller, [59], who — for the sake of an application to nonlinear elasticity — proved that if the Jacobian determinant Ju of a Sobolev map u ∈ W 1,n loc (Rn ,Rn ) is nonnegative, then it belongs locally to L log L. The result is quite intriguing, since a priori Hölder inequality implies only that Ju ∈ L1 and one does not suspect any higher integrability. If one ...

Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces

Harmonic maps between three-spheres

It is shown that smooth maps f : S → S contain two countable families of harmonic representatives in the homotopy classes of degree zero and one.

Remarks on biharmonic maps into spheres

We prove an apriori estimate in Morrey spaces for both intrinsic and extrinsic biharmonic maps into spheres. As applications, we prove an energy quantization theorem for biharmonic maps from 4-manifolds into spheres and a partial regularity for stationary intrinsic biharmonic maps into spheres. x