Let $u:B_{2r}(x)\to\mathds{R}$ be a harmonic function with $r\leq 1$. Then for every $\epsilon>0$ there exists $\delta(n,\epsilon)>0$ such that if ${\rm Ric}_{M^{n}}\geq-(n-1)\delta^{2}$ and

$\displaystyle r^{2}\fint_{B_{2r}(x)}|\Delta|\nabla u||\leq\delta\fint_{B_{2r}(x)}|\nabla u|\,,$

(3.23)

then for $A=\Big(\fint_{B_{r}(x)}|\nabla u|\Big)^{-1}>0$ we have that $A\circ u:B_{r}(x)\to\mathds{R}$ is an $\epsilon$-splitting map.