Limiting behaviour of the Ricci flow

Abstract

We will consider a {\it $\tau$-flow}, given by the equation $\frac{d}{dt}{g}_{ij}=-2R_{ij}+\frac{1}{\tau }{g}_{ij}$ on a closed manifold $M$, for all times $t\in [0,\infty )$. We will prove that if the curvature operator and the diameter of $(M,g(t))$ are uniformly bounded along the flow, then we have a sequential convergence of the flow toward the solitons.

Cited by in corpus (2)

• Convergence of the Ricci flow toward a unique soliton
• The Kähler-Ricci flow on Kähler manifolds with 2 traceless bisectional curvature operator