Harmonic maps between three-spheres

Twistor Interpretation of Harmonic Spheres and Yang–Mills Fields

We consider the twistor descriptions of harmonic maps of the Riemann sphere into Kähler manifolds and Yang–Mills fields on four-dimensional Euclidean space. The motivation to study twistor interpretations of these objects comes from the harmonic spheres conjecture stating the existence of the bijective correspondence between based harmonic spheres in the loop space ΩG of a compact Lie group G a...

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...

Some Recent Developments in the study of minimal 2-spheres in spheres

We discuss recent progress in the study of the space of harmonic maps from the 2sphere to the unit n-sphere in Euclidean (n+1)-space. We consider the structure of this space as an algebraic variety, the existence of non-manifold points in this space, and the relation between this question and the integrability of Jacobi fields along harmonic maps. One of the main tools used is that of the twist...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

F-harmonic Maps as Global Maxima

In this note, we show that some F -harmonic maps into spheres are global maxima of the variations of their energy functional on the conformal group of the sphere. Our result extends partially those obtained in [15] and [17] for harmonic and p-harmonic maps.