Stability and singularities of harmonic maps into 3-spheres Original Research Article

The behavior of harmonic maps from a domain in View the MathML source into View the MathML source is discussed. In this paper, we show that if u is a strictly stable stationary harmonic map : View the MathML source, such that the singular set Sing(u) of u consists of {0}, then the degree deg(u,0) of u at 0 is zero; and that if u is a weakly stable harmonic map View the MathML source with Sing(u)={0}, then deg(u,0)=0 or ±1. Furthermore, the characterization of homogeneous stable stationary harmonic maps from View the MathML source into View the MathML source is given.