Time-dependent Sobolev inequality along the Ricci flow

Abstract

In this article we get a time-dependent Sobolev inequality along the Ricci flow which generalizes the earlier results of Zhang, Ye, Hsu. As an application of the time-dependent Sobolev inequality, we also get a growth of the ratio of bob-collapsing along the Ricci flow.

Proof of Theorem 2.2 is added, a serious mistake in the proof of Theorem 2.3 is corrected