International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 30, Pages 1599-1611

Minimizing energy among homotopic maps

Pengzi Miao

Department of Mathematics, Stanford University, Palo Alto 94305, CA, USA

Received 6 May 2003

Copyright © 2004 Pengzi Miao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study an energy minimizing sequence {ui} in a fixed homotopy class of smooth maps from a 3-manifold. After deriving an approximate monotonicity property for {ui} and a continuous version of the Luckhaus lemma (Simon, 1996) on S2, we show that, passing to a subsequence, {ui} converges strongly in W1,2 topology wherever there is small energy concentration.