For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S k . We show that the singular set of stable-stationary harmonic maps from B 5 to S 3 is the union of finitely many isolated singular points and finitely many Hölder continuous curves. We also discuss the minimization problem among continuous maps from B n to S 2.
- Hausdorff dimension
- Stable stationary harmonic map
ASJC Scopus subject areas
- Applied Mathematics