Isoperimetric estimate for the Ricci flow on S-2 x S-1

摘要

In this paper, we study the dilation limit of S-2 X S-1 with a warped product metric under the Ricci flow. We first prove that the isoperimetric ratio on the base manifold S-2 has a lower bound, which excludes the Sigma(2) x R as the dilation limit. We also prove a monotonicity result under a certain condition.