Methods and Applications of Analysis

Volume 9 (2002)

Number 3

A Lioville Type Theorem for Minimizing Maps

Pages: 407 – 424



Fengbo Hang

Fanghua Lin


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.

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