Continuous rational maps into spheres

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

Remarks on biharmoni maps into spheres

Rational Homotopy of Spaces of Maps Into Spheres and Complex Projective Spaces

We investigate the rational homotopy classification problem for the components of some function spaces with Sn or cPn as target space.

Stability and singularities of harmonic maps into spheres

On polyharmonic maps into spheres in the critical dimension

We prove that every polyharmonic map u ∈ W(B, SN−1) is smooth in the critical dimension n = 2m. Moreover, in every dimension n, a weak limit u ∈ W(B, SN−1) of a sequence of polyharmonic maps uj ∈ W(B, SN−1) is also polyharmonic. The proofs are based on the equivalence of the polyharmonic map equations with a system of lower order conservation laws in divergence-like form. The proof of regularit...