Stable Stationary Harmonic Maps to Spheres

Energy Quantization for Harmonic Maps

In this paper we establish the higher-dimensional energy bubbling results for harmonic maps to spheres. We have shown in particular that the energy density of concentrations has to be the sum of energies of harmonic maps from the standard 2dimensional spheres. The result also applies to the structure of tangent maps of stationary harmonic maps at either a singularity or infinity. 0. Introductio...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Remarks on biharmonic maps into spheres

We prove an apriori estimate in Morrey spaces for both intrinsic and extrinsic biharmonic maps into spheres. As applications, we prove an energy quantization theorem for biharmonic maps from 4-manifolds into spheres and a partial regularity for stationary intrinsic biharmonic maps into spheres. x

Gradient estimates and blow - up analysis for stationary harmonic maps

For stationary harmonic maps between Riemannian manifolds, we provide a necessary and sufficient condition for the uniform interior and boundary gradient estimates in terms of the total energy of maps. We also show that if analytic target manifolds do not carry any harmonic S2, then the singular sets of stationary maps are m ≤ n− 4 rectifiable. Both of these results follow from a general analys...

Stable Harmonic 2-spheres in Symmetric Spaces

TO = \ I l̂ l'vol. * J M A harmonic map 0 is said to be stable if the second variation of E at (j> is positive semidefinite. That is: for all smooth variations t)\t=0 > 0. Of particular interest is the case where M is the sphere S and N is a Riemannian symmetric space G/K. In this setting harmonic maps are branched minimal immersions, or the finite ...