Qi S. Zhang
Using a size condition of the sharp log Sobolev functional (log entropy) near infinity only, we prove a rigidity result for ancient Ricci flows without sign condition on the curvatures. The result is also related to the problem of identifying type II ancient Ricci flows and their backward limits.
Qi S. Zhang
This paper contains 2 sections, 7 theorems, 138 equations.
Theorem \oldthetheorem
There exists a positive number $\epsilon_0$, depending only on the dimension $n (\ge 3)$ such that the following is true. Let $(M, g(t), x_0)$, $\partial_t g_{ij} = - 2 R_{ij}$, $t \in (-\infty, 0]$ be a complete, noncompact Ricci flow with bounded curvature, which is $\kappa$ non-collapsed at scale holds for all $t \le 0$, then $(M, g(t))$ is the standard $\mathbf{R^n}$. The converse is also true
