A note on the nonexistence of quasi-harmonic spheres

2016/04/10 by Li, Jiayu, Sun, Linlin
#53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.02696

Abstract

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 ρ with the exponential growth condition ρ(y)≤ Cexp(\frac14 d(y)^2/m) where d(y) is the distance function on N, then N does not admit a quasi-harmonic sphere, which generalize Li-Zhu's result \citeLi2010non. We also show that if u is a quasi-harmonic sphere, then the property that u is of finite energy (∫_\R^me(u)e^-\absx²/4\dif x

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