A gap theorem for α-harmonic maps between two-spheres

A Structure Theorem of Dirac-harmonic Maps between Spheres

For an arbitrary Dirac-harmonic map (φ, ψ) between compact oriented Riemannian surfaces, we shall study the zeros of |ψ|. With the aid of Bochner-type formulas, we explore the relationship between the order of the zeros of |ψ| and the genus of M and N . On the basis, we could clarify all of nontrivial Dirac-harmonic maps from S to S.

Harmonic maps between three-spheres

It is shown that smooth maps f : S → S contain two countable families of harmonic representatives in the homotopy classes of degree zero and one.

A Liouville theorem for harmonic maps and

A Liouville theorem is proved which generalizes the papers of Hu, MP].

Stable Stationary Harmonic Maps to Spheres

Dedicated to Professor WeiYue Ding on the occasion of his 60th birthday Abstract For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S. We show that the singular set of stable-stationary harmonic maps from B to S is the union of finitely many isolated singular points and finitely many Hölder continuous curves. We also...

Stable Exponentially Harmonic Maps Between Finsler Manifolds