A note on the nonexistence of quasi-harmonic spheres

作者：Li, Jiayu^*; Sun, Linlin

来源：Calculus of Variations and Partial Differential Equations, 2016, 55(6): 151.

DOI：10.1007/s00526-016-1076-6

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In this paper we study the properties of quasi-harmonic spheres from R-m, m > 2. We show that if the universal covering N of N admits a nonnegative strictly convex function p with the exponential growth condition p(y) <= C exp (1/4d(y)(2/m) where d(y) is the distance function on N, then does not admit a quasi -harmonic sphere, which generalize Li-Zhu's result (Calc Var Partial Diff Equ 37(3-4):441-460, 2010). We also show that if u is a quasi -harmonic sphere, then the property that u is of finite energy (integral R(m)e(u)e(-vertical bar x vertical bar 2/4)dx < infinity) is equivalent to the property that u satisfies the large energy condition (lim(R) infinity, R(m)e-R-2/4 integral Br(0) e(u)e-(vertical bar x vertical bar 2/4)dx =0)

• 出版日期2016-12
• 单位中国科学技术大学