Erratum to: A Uniform Sobolev Inequality Under Ricci Flow

Abstract

In the paper [3], the constants in Theorem 1.1 (a) should depend on time in general. Here, we provide the corrected statement and proof. “A uniform Sobolev inequality under Ricci flow”, the constants A and B of Theorem 1.1 (a) are correct only for finite time. For large time t, they should depend on time t via the controlling constants in the log Sobolev inequality of the metric t g(0), which is finite only sometimes. Step 2 of the proof should follow the method outlined at the end of the introduction instead. Here is the corrected statement for that theorem.