A $\epsilon$-splitting map $u=(u^{1},\ldots,u^{k}):B_{r}(p)\to\mathds{R}^{k}$ is a harmonic map such that:

1. (1)

   $|\nabla u|\leq 1+\epsilon$.

2. (2)

   $\fint_{B_{r}(p)}|\langle\nabla u^{\alpha},\nabla u^{\beta}\rangle-\delta^{\alpha\beta}|^{2}<\epsilon^{2}$.

3. (3)

   $r^{2}\fint_{B_{r}(p)}|\nabla^{2}u^{\alpha}|^{2}<\epsilon^{2}$.