Boundary Regularity of Weakly Harmonic Maps from Surfaces

Regularity for weakly Dirac-harmonic maps to hypersurfaces

We prove that a weakly Dirac-harmonic map from a Riemann spin surface to a compact hypersurface N ⊂ R is smooth. 2000 Mathematics Subject Classification: 58J05, 53C27.

Regularity of Harmonic Maps

Boundary Regularity and the Dirichlet Problem for Harmonic Maps

In a previous paper [10] we developed an interior regularity theory for energy minimizing harmonic maps into Riemannian manifolds. In the first two sections of this paper we prove boundary regularity for energy minimizing maps with prescribed Dirichlet boundary condition. We show that such maps are regular in a full neighborhood of the boundary, assuming appropriate regularity on the manifolds,...

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...

Regularity for n-Harmonic Maps

§