The regularity of conformal target harmonic maps

Regularity of Harmonic Maps

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

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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,...

A geometric theory of harmonic and semi-conformal maps

We describe for any Riemannian manifold M a certain scheme ML, lying in between the first and second neighbourhood of the diagonal of M . Semiconformal maps between Riemannian manifolds are then analyzed as those maps that preserve ML; harmonic maps are analyzed as those that preserve the (LeviCivita-) mirror image formation inside ML. Introduction For any Riemannian manifold M , we describe a ...