  Nonexistence of quasi-harmonic spheres is necessary for long time existence
and convergence of harmonic map heat flows. Let $(N,h)$ be a complete
noncompact Riemannian manifolds. Assume the universal covering of $(N,h)$
admits a nonnegative strictly convex function with polynomial growth. Then
there is no quasi-harmonic spheres $u:\mathbb{R}^n\ra N$ such that
$$\lim_{r\ra\infty}r^ne^{-\f{r^2}{4}}\int_{|x|\leq r}e^{-\f{|x|^2}{4}}|\nabla
u|^2dx=0.$$ This generalizes a result of the first named author and X. Zhu
(Calc. Var., 2009). Our method is essentially the Moser iteration and thus very
simple.
