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In this paper we study the properties of quasi-harmonic spheres from $$\mathbb {R}^m, m>2$$Rm,m>2. We show that if the universal covering $$\tilde{N}$$N~ of N admits a nonnegative strictly convex function $$\rho $$ρ with the exponential growth condition $$\rho (y)\le C\exp \left( \frac{1}{4}\tilde{d}(y)^{2/m}\right) $$ρ(y)≤Cexp14d~(y)2/m where $$\tilde{d}(y)$$d~(y) is the distance function on $$\tilde{N}$$N~, then N 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 ($$\int _{\mathbb {R}^m}e(u)e^{-\left|x\right|^2/4}\mathrm dx<\infty $$∫Rme(u)e-x2/4dx<∞) is equivalent to the property that u satisfies the large energy condition ($$\lim _{R\rightarrow \infty }R^{m}e^{-R^2/4}\int _{B_R(0)}e(u)e^{-\left|x\right|^2/4}\,\mathrm dx=0$$limR→∞Rme-R2/4∫BR(0)e(u)e-x2/4dx=0).

A note on the nonexistence of quasi-harmonic spheres