Here we establish a Liouville type theorem for minimizing maps from R2 (or in general, from Rm) into a compact Riemannian manifold N. As a consequence of this, we prove a local gradient estimate for minimal solutions to a variational problem arise from planar ferromagnetism and anti-ferromagnetism. The latter can be applied to study the asymptotic behavior of entire solutions.
"A Lioville Type Theorem for Minimizing Maps." Methods Appl. Anal. 9 (3) 407 - 424, September 2002.