A counterexample to the second inequality of Corollary (19.10) in the monograph "Ricci Flow and the Poincare Conjecture" by J.Morgan and G.Tian

TL;DR

This paper presents a counterexample to a specific inequality in Morgan and Tian's monograph on Ricci flow, challenging a previously accepted mathematical statement and providing detailed evidence for this exception.

Contribution

The authors construct and detail a counterexample to the second inequality of Corollary 19.10 in Morgan and Tian's Ricci flow monograph, clarifying a mathematical misconception.

Findings

Counterexample invalidates the second inequality of Corollary 19.10

Details of the counterexample are explicitly provided

Discussion of the correction by Morgan and Tian is forthcoming

Abstract

We provide here a counter-example to the second inequality of Corollary (19.10) in the Clay Institute Monograph by J.Morgan and G.Tian entitled "Ricci Flow and the Poincare Conjecture". We had announced the existence of this counter-example in our paper "Five Gaps in Mathematics", Advanced Non-linear Studies, vol 15, No. 2, (2015). We make the details available here. J.Morgan and G.Tian have recently (arXiv/math/DG:1512.00699, (2015)) published a correction to their arguments in the monograph. In a forthcoming short Note, we will discuss this correction. We wish to thank John Morgan, Terry Tao and Gang Tian for having considered and discussed the validity of this counter-example.