Methods and Applications of Analysis

Volume 9 (2002)

Number 3

A Lioville Type Theorem for Minimizing Maps

Pages: 407 – 424

DOI: https://dx.doi.org/10.4310/MAA.2002.v9.n3.a7

Authors

Fengbo Hang

Fanghua Lin

Abstract

Here we establish a Liouville type theorem for minimizing maps from R² (or in general, from R^m) 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.

Published 1 January 2002