Convergence of Finslerian metrics under Ricci flow

Abstract

In this work, convergence of evolving Finslerian metrics first in a general flow next under Finslerian Ricci flow is studied. More intuitively it is proved that a family of Finslerian metrics $g(t)$ which are solutions to the Finslerian Ricci flow converge in $C^{\infty }$ 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 Ricci flow blows up in short time.

Accepted for Publication in Science China Mathematics (2015)

Cited by in corpus (2)

• Ricci flow on Finsler surfaces
• Complete Ricci solitons on Finsler manifolds