Some conformal properties of p-harmonic maps and a regularity for sphere-valued p-harmonic maps

Regularity of generalized sphere valued p - harmonic maps with small mean oscillations

We prove (see Theorem 1.3 below) that a generalized harmonic map into a round sphere, i.e. a map u ∈ W 1,1 loc ( , Sn−1) which solves the system div (ui∇uj − uj∇ui) = 0, i, j = 1, . . . , n, is smooth as soon as |∇u| ∈ L for any q > 1, and the norm of u in BMO is sufficiently small. Here, ⊂ R is open, and m, n are arbitrary. This extends various earlier results of Almeida [1], Ge [15], and R. M...

Regularity of Harmonic Maps

Regularity for n-Harmonic Maps

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Regularity of Dirac-harmonic maps

For any n-dimensional compact spin Riemannian manifold M with a given spin structure and a spinor bundle ΣM , and any compact Riemannian manifold N , we show an ǫ-regularity theorem for weakly Dirac-harmonic maps (φ, ψ) : M ⊗ΣM → N ⊗ φ∗TN . As a consequence, any weakly Dirac-harmonic map is proven to be smooth when n = 2. A weak convergence theorem for approximate Dirac-harmonic maps is establi...

Existence and regularity results for the gradient flow for p - harmonic maps ∗

We establish existence and regularity for a solution of the evolution problem associated to p-harmonic maps if the target manifold has a nonpositive sectional curvature.