Graphical mean curvature flow with bounded bi-Ricci curvature

We consider the graphical mean curvature flow of strictly area decreasing maps $f:M\to N$, where $M$ is a compact Riemannian manifold dimension $m>1$ and $N$ complete surface bounded geometry. prove long-time existence that property preserved, when bi-Ricci $BRic_M$ from below by sectional $\sigma_N$ $N$. In addition, we obtain smooth convergence to minimal map if $Ric_M\ge\sup\{0,{\sup}_N\sigma_N\}$. These results significantly improve known on in codimension $2$.