对于Lott的质疑,曹怀东的回信实在无力.曹说"By "we avoid using his crucial estimate in Claim 2 in Section 12.1 of [103]", we don't mean we are providing an "original alternative argument".".这是狡辩.在曹朱的文章里说:"我们想指出我们关于奇点结构定理（定理 7.1.1 ）的证明与佩雷尔曼的证明有二点不同: 第 （1） 我们避免了使用他在 [ 103 ] 中12.1节claim 2里的一个关键性估计; ...",这话的意思显然就是他们用了新的方法来证明.曹怀东的信这样否认连外行也蒙不了.而且重要的是,曹怀东一点也不提Lott对他们抄袭Lott的质疑"In fact, the alternative argument presented on pages 400-402 is essentially the same as the one in our "Notes on Perelman's Paper".这个质疑才是最关键重要的,曹怀东竟然想在这上面脚底抹油溜之大吉.不难想象Lott收到这信后的感受,他肯定会认为曹怀东是个很不诚实的人.即使现在曹朱在更大的压力之下道歉了,Lott也会认为他们并不诚恳,看来他们的道歉也确实是不够诚恳的,怪不得有传言说Lott认为朱熹平不诚实,拒绝和朱在同一天作讲演,从而使美国数学会取消一个special event.曹怀东承认是"followed Perelman",倒不敢去抢credit.对于Lott质疑的"Furthermore, pages 400-402 of your paper reproduce entire passages from our notes, with minor modifications", 曹基本承认他们的文章pages 400-402 和Lott的Notes实质上相同:"your Notes and our paper have essentially the same notations and some similar phrases or terminologies.",后面又辩解一下,但这已经不重要.
From: [email protected]
Reply-To: [email protected]
Subject: Re: your paper
To: John lott
Cc: [email protected], [email protected], [email protected]
Dear John,
Please excuse me for not replying your email sooner. I have beenon vacation.Below I try to address your point of concern:By "we avoid using his crucial estimate in Claim 2 in Section 12.1 of[103]", we don't mean we are providing an "original alternativeargument". The factis that we didn't understand the proof of Perelman's Claim 2, but his arguments could prove a weaker version of it, namely finitedistanceimplies finite curvature. So we view this part in our paper asfillingin Perelman's argument with some minor modifications. I aminterestedto know if you think Perelman has any serious mistake here?Since we all followed Perelman, I am not surprised that your Notesand ourpaper have essentially the same notations and some similar phrasesorterminologies. Comparing your Notes and our paper, one couldnoticethere are many differences in our arguments. For example:1. You take the pointed Gromov-Hausdorff limit for the sequences$（B（x_k,\rho_0）,\bar g_k（t_k）,x_k）$, while we take$C^{\infty}_{loc}$limit so that the limit is still a solution.
We also noticed that you included some additional argument, part 4 of Corollary 33.1, to btain the smoothness. Since the contradiction comes from Hamilton's strong maximum principle to smooth solutions of the Ricci flow, we triedtokeep the limit in the smooth category.2. To show the limit metric is cylindrical at points close to thet ip,you established a lemma; while we used the canonical neighborhood structure to exclude the possibility of $2\varepsilon$-cap. In our paper, we took two paragrphes about 1/4 of the Step 2to show this.3. To show the tangent cone is nonflat, you used your lemma 43.5;while we used the smallness of aperture. As you knew, the nonflatness of thetangent cone was used to derive the contradiction to the strongmaximumprinciple. We also use the nonflatness to show theGromov-Hausdorfflimit tothe tangent cone coincides with the associated smooth limt. We pays pecial attention to the relation between Gromov-Hausdorff limits andsmooth limits.etc.I am sorry that you are not satisfied with the way we acknowledged your Notes. We will make attempt to pay more attention to make youhappyinfuture.I hope the above help to clarify the matter.
Best, Huai-Dong
Quoting John lott :
Dear Huai-Dong,
I wrote to you a week ago about an issue concerning your paper with Zhu. So far I have not received a response. Bruce and I view this as a serious matter. If we do not hear from you or Xi-ping Zhu by onday, July 31, then we will assume that you do not intend to respond.
Yours truly,John
On Wed, 19 Jul 2006, John lott wrote:
Dear Huai-Dong,
Thank you for sending the copy of your paper. I havenot had time to read all of it yet, but am puzzled aboutthe following point.In the introduction it is written "We would like topoint out that our proof of the singularity structure theoremTheorem 7.1.1
is different from that of Perelman in twoaspects: 1
we avoid using his crucial estimate in Claim 2 inSection 12.1 of [103]; 2
we give a new approach to extendthelimit backward in time to an ancient solution. Thesedifferences are due to the difficulties inunderstanding Perelman's arguments at these points."
In so writing, it is implied that you are providing anoriginal alternative argument to deal with Perelman'sClaim 2. In fact, the alternative argument presented on pages400-402 is essentially the same as the one inour "Notes on Perelman's Paper", which was first posted on our website
http://www.math.lsa.umich.edu/research/ricciflow/perelman.html
in June of 2003.
This part of the Notes was not changedin later versions. The February 2004 version, and somesubsequent versions, can be seen on the Wayback Machine at
http://web.archive.org/web/*/
http://www.math.lsa.umich.edu/research/ricciflow/perelman.html
The only mention of our Notes in your paper seems to be thesentence in the introduction "We remark that there have also appeared several sets of notes on Perelman's work, including theone written by B. Kleiner and J. Lott [78], which cover part ofthe materials that are needed for the geometrization program."
In particular, the alternative argument for Claim 2 ispresented as in your paper as original work, and is notattributed to Bruce and me.Furthermore, pages 400-402 of your paper reproduce entirepassages from our notes, with minor modifications. Attachedare files c.dvi and c.pdf with a side-by-side comparison. Theleft hand column is from the June 2003 version of our notes.The right hand column is from your paper. The material inoldface was copied, again without proper attribution. Nosimilar phrases appear in Perelman's paper.I am quite disturbed by this and await your explanation.
Yours truly,
John
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