Convergence of Finslerian metrics under Ricci flow (Q294510)

The authors prove that a family of Finslerian metrics \(g(t)\), which are solutions to the geometric flow \({{\partial}\over {\partial t}}g(t)=\omega (t)\), converges in \(C^\infty\) to a smooth limit Finslerian metric \(\bar g\), as \(t\) approaches \(T\). They also show that on a compact manifold, a family of solutions to the Finslerian Ricci flow \({{\partial}\over {\partial t}}g_{j_k}(t)=-2\mathrm{Ric}_{j_k}\) converges in \(C^\infty\) to a smooth limit Finslerian metric \(\bar g\), as \(t\) approaches \(T\). They use this result to prove that in a compact Finsler manifold the Ricci flow cannot develop a singularity in finite time unless the \(hh\)-curvature is bounded.