Mathematical Research Letters

Volume 22 (2015)

Number 2

Mean value inequalities and conditions to extend Ricci flow

Pages: 417 – 438



Xiaodong Cao (Department of Mathematics, Cornell University, Ithaca, New York, U.S.A.)

Hung Tran (Department of Mathematics, University of California at Irvine)


This paper concerns conditions related to the first finite singularity time of a Ricci flow solution on a closed manifold. In particular, we provide a systematic approach to the mean value inequality method, suggested by N. Le [13] and F. He [11]. We also display a close connection between this method and time slice analysis as in [23]. As an application, we prove several inequalities for a Ricci flow solution on a manifold with nonnegative isotropic curvature.

2010 Mathematics Subject Classification


Published 16 April 2015