Stationary p-harmonic maps into spheres

Stable Stationary Harmonic Maps to Spheres

Dedicated to Professor WeiYue Ding on the occasion of his 60th birthday Abstract For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S. We show that the singular set of stable-stationary harmonic maps from B to S is the union of finitely many isolated singular points and finitely many Hölder continuous curves. We also...

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.