No neck for approximate harmonic maps to the sphere

作者：Zhu Xiangrong^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2012, 75(11): 4339-4345.

DOI：10.1016/j.na.2012.03.020

• Harmonic map
• Tension field
• Orlicz space
• Zygmund class

In this paper, we consider a sequence of maps from a Riemann surface to a standard sphere with tension fields bounded in an Orlicz space phi(L) where
phi(L) = {f : integral phi(vertical bar f vertical bar) < infinity}.
If there holds
lim(t ->infinity)phi(t)/t lnt=infinity,
we can prove that there is no neck during blow up. This result improves our previous theorems in Li and Zhu [1,2]. One can see that our result here is optimal in the size conditions.

• 出版日期2012-7
• 单位浙江师范大学