Uniformly trivial 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

Uniformly approachable maps∗

Throughout the paper we will use the standard definitions and notation ([ABR], [E]). Let X and Y be metric spaces. The goal is to study some intermediate classes of functions between the class Cuc(X,Y ) of all uniformly continuous mappings (briefly, UC) from X into Y and the class C(X,Y ) of all continuous functions f :X → Y . These classes, defined below, have been intensively studied in [BD] ...

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...