Convergence of Finslerian metrics under Ricci flow

In this work, we study the convergence of evolving Finslerian metrics first in a general flow and next under Finslerian Ricci flow. More intuitively it is proved that a family of Finslerian metrics g(t) which are solutions to the Finslerian Ricci flow converges in C^∞ to a smooth limit Finslerian metric as t approaches the finite time T. As a consequence of this result one can show that in a compact Finsler manifold the curvature tensor along the Ricci flow blows up in a short time.