Quantitative regularity for $p$-harmonic maps

Regularity for n-Harmonic Maps

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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...

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.

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.