From http://www.doctoryau.com/

Dear Mr. Cooper,

I am very disturbed by the unfair manner in which Yau Shing-Tung has
been portrayed in the New Yorker article. I am providing my thoughts
below to set the record straight. I authorize you to share this
letter with the New Yorker and the public if that will be helpful to
Yau. As soon as my first paper on the Ricci Flow on three
dimensional manifolds with positive Ricci curvature was complete in
the early '80's, Yau immediately recognized it's importance;and
although I had proved a result on which he had been working with
minimal surfaces,rather than exhibit any jealosy he became my
strongest supporter.He pointed out to me way back then that the
Ricci Flow would form the neck pinch singularities,undoing the
connected sum decomposition,and that this could lead to a proof of
the Poincare conjecture. In 1985 he brought me to UC San Diego
together with Rick Schoen and Gerhard Huisken,and we had a very
exciting and productive group in Geometric Analysis. Huisken was
working on the Mean Curvature Flow for hypersurfaces, which closely
parallels the Ricci Flow,being the most natural flows for intrinsic
and extrinsic curvature respectively. Yau repeatedly urged us to
study the blow-up of singularities in these parabolic equations
using techniques parallel to those developed for elliptic equations
like the minimal surface equation,on which Yau and Rick are experts.
Without Yau's guidance and support at this early stage, there would
have been no Ricci Flow program for Perelman to finish.

Yau also had some outstanding students at San Diego who had come
with him from Princeton, in particular Cao Huai-Dong, Ben Chow and
Shi Wan-Xiong. Yau encouraged them to work on the Ricci Flow,and all
made very important contributions to the field. Cao proved existence
for all time for the normalized Ricci Flow in the canonical Kaehler
case ,and convergence for zero or negative Chern class.Cao's results
form the basis for Perelman's exciting work on the Kaehler Ricci
Flow,where he shows for positive Chern class that the diameter and
scalar curvature are bounded. Ben Chow, in addition to excellent
work on other flows, extended my work on the Ricci Flow on the two
dimensional sphere to the case of curvature of varying sign. Shi
Wan-Xiong pioneered the study of the Ricci Flow on complete
noncompact manifolds,and in addition to many beautiful arguments he
proved the local derivative estimates for the Ricci Flow.The blow-up
of singularities usually produces noncompact solutions,and the proof
of convergence to the blow-up limit always depends on Shi's
derivative estimates; so Shi's work is central to all the limit
arguments Perelman and I use.

In '82 Yau and Peter Li wrote an exceedingly important paper giving
a pointwise differential inequality for linear heat equations which
can be integrated along curves to give classic Harnack inequalities.
Yau repeatedly urged me to study this paper,and based on their
approach I was able to prove Harnack inequalities for the Ricci Flow
and for the Mean Curvature Flow. This Harnack inequality,generalized
from Li-Yau, forms the basis for the analysis of ancient solutions
which I started, and which Perelman completed and uses as the basic
tool in his canonical neighborhood theorem. Cao Huai-Dong proved the
Harnack estimate for the Ricci Flow in the Kahler case,and Ben Chow
did the same for the Yamabe Flow and the Gauss Curvature Flow. But
there is more to this story. Perelman's most important is his
noncol-lapsing result for Ricci Flow,valid in all dimensions,not
just three,and thus one whose importance for the future extends well
beyond the Poincare conjecture,where it is the tool for ruling out
cigars,the one part of the singularity classification I could not
do. This result has two proofs,one using an entropy for a backward
scalar heat equation,and one using a path integral.The entropy
estimate comes from integrating a Li-Yau type differential Harnack
inequality for the adjoint heat equation,and the other is the
optimal Li-Yau path integral for the same Harnack inequality; as
Perelman acknowledges in 7.4 of his first paper,where he writes "an
even closer reference is [L-Y],where they use ``length" associated
to a linear parabolic equation,which is pretty much the same as in
our case".

Over the years Yau has consistently supported the Ricci Flow and the
whole field of Geometric Flows,which has other important successes
as well,such as the recent proof of the Penrose Conjecture by
Huisken and Ilmanen,a very important result in General Relativity. I
cannot think of any other prominent leader who gave nearly support
to our field as Yau has.

Yau has built is an assembly of talent, not an empire of power,
people attracted by his energy, his brilliant ideas, and his
unflagging support for first rate mathematics, people whom Yau has
brought together to work on the hardest problems.Yau and I have
spent innumerable hours over many years working together on the
Ricci Flow and other problems, often even late at night. He has
always generously shared his suggestions with me, starting with the
observation of neck pinches,never asking for credit. In fact just
last winter when I finally managed to prove a local version of the
Harnack inequality for the Ricci Flow, a problem we had worked on
together for many years, and I said I ought to add his name to the
paper,he modestly declined.It is unfortunate that his character has
been so badly misrepresented. He has never to my knowledge proposed
any percentages of credit,nor that Perelman should share credit for
the Poincare conjecture with anyone but me; which is reasonable,as
indeed no one has been more generous in crediting my work than
Perelman himself.F ar from stealing credit for Perelman's
accomplishment, he has praised Perelman's work and joined me in
supporting him for the Fields Medal. And indeed no one is more
responsible than Yau for creating the program on Ricci Flow which
Perelman used to win this prize.

Sincerely yours,
Richard S Hamilton
Professor of Mathematics,
Columbia University

a very good letter
thanks a lot

以下是中国科学院刊出的译文：

汉密尔顿致丘成桐代理律师的信

科学时报


尊敬的库珀先生：

丘成桐在《纽约客》的文章被以不公正的方式描写让我感到极大的不安。我在下面提供给你我关于此事的看法，以正视听。我授权你在能够对丘有所帮助的情况下将这封信与《纽约客》杂志和公众分享。

20世纪80年代初，在我刚完成具有正瑞奇（Ricci）曲率的三维流形瑞奇流的第一篇论文时，丘立刻意识到了它的重要性。虽然我证明了一个他一直在用极小曲面从事研究的结果，他不仅没有表现出任何嫉妒之意，而是成为我最有力的支持者。早在当时，他就向我指出瑞奇流可以形成瓶颈（neck pinch）奇点，这些奇点会解决连通和分解的问题，这样就可以导致庞加莱猜想的一个证明。1985年，他把我、Rick Schoen（注：现Stanford大学数学系教授）和Gerhard Huisken（注：现德国马克斯－普朗克引力物理研究所所长）一起带到了加州大学圣地亚哥分校，我们四人形成了一个非常活跃且颇具成效的几何分析研究小组。当时Huisken主攻超曲面的平均曲率流，这是一个几乎和Ricci流平行的研究方向，也是对内蕴和外蕴曲率来说最自然的几何流。丘成桐反复鼓励我们用一些类似于椭圆方程研究中发展出来的极小曲面方程中的技巧来研究这些抛物方程中奇异点的放大问题。在极小曲面方程方面，丘与Rick是该方面的专家。如果没有丘成桐早期的指导和支持，就不会发展出整套的Ricci流纲领，Perelman最后完成的正是这一纲领。

丘还有一些跟随他从普林斯顿到圣地亚哥分校的非常杰出的学生，特别是曹怀东，周培能和施皖雄三人。丘成桐鼓励他们研究瑞奇流，他们对这个领域也作出了非常重要的贡献。曹怀东证明了在正则Kaehler情形中归一化瑞奇流总是具有存在性，并具有对零或负的陈类的收敛性。曹怀东的结果是佩雷尔曼在Kaehler瑞奇流研究中激动人心的工作的基础，佩雷尔曼证明了瑞奇流对于正的陈类半径与标度曲率是有界的。周培能除了在其他几何流方面有很多杰出的工作之外，还把我在二维球上瑞奇流的工作推广到了曲率可变号的情形。施皖雄开创了完整非紧流形上瑞奇流的研究，在许多漂亮的论证基础上他证明了瑞奇流的局部微商估计。奇异点的放大通常会产生非紧致解，证明放大极限的收敛性总是要依赖于施皖雄的微商估计，所以施皖雄的工作是佩雷尔曼和我使用的所有极限论证方法的关键。

1982年，丘成桐和李伟光（Peter Li）写了一篇超乎寻常重要的论文，文章给出了线性热方程的逐点微分不等式，它在沿曲线积分后可以给出经典的Harnack不等式。丘成桐反复地鼓励我研究这篇论文，基于他们的方法，我得以证明瑞奇流和平均曲率流的Harnack不等式。这种由李-丘的工作所得到的Harnack不等式是对我开创的早先的解决方案进行分析的基础。Perelman完成了这一分析，并且这正是他的正则邻域定理中所用到的基本工具。曹怀东证明了Kaehler情形中瑞奇流的Harnack估计，而周培能则证明了Yamabe流和高斯曲率流的Harnack估计。

故事远还没有结束于此。佩雷尔曼最重要的工作是瑞奇流非坍塌性结果不仅仅在三维而且在任意维数中都有效。它对未来的意义超出了庞加莱猜想本身，这成为了排除雪茄型奇点的工具，而雪茄型奇点正是我未能解决的一种奇异点分类。这个结果有两个证明，一个使用了逆向标量热方程的熵，另一个使用了路径积分。这里对熵的估计来自于对共轭热方程的李-丘微分型Harnack不等式的积分，另一种估计是对同样的Harnack不等式的最优李-丘路径积分。正如佩雷尔曼在他的第一篇论文7.4节中的所承认的，他写道：“一个更为相关的参考文献是[L-Y]，这里他们所用的一个与线性抛物方程相关的‘长度’，这与我们的情形几乎一模一样”。

多年来，丘成桐一致不懈地支持瑞奇流和整个几何流领域的研究。这些研究还导致了其他重要的成就，比如最近Huisken和Ilmanen对Penrose猜想的证明，这是广义相对论中非常重要的结果。我不认为除丘之外还有能够对我们的领域给以如此之多的支持的卓越领袖。

丘建立的是一个天才的团队，而不是权力的帝国。人们被他的活力、睿智和他对一流数学家坚定不移的支持所吸引，丘成桐将他们聚集在一起攻克最难的问题。在过去的许多年里，丘和我在瑞奇流和其他问题上一起度过了无数时间，常常是工作到深夜。从研究瓶颈奇点时开始，他就一贯无私地与我分享他的建议与意见，而从不要求得到任何个人荣誉。事实上，就在去年冬天，当我最后证明了一个我们一起研究多年的问题，即瑞奇流的Harnack不等式的局部情形，我提出应该将他的名字也写进论文，他却谦虚地谢绝了。不幸的事情是，现在他的人品被这样不合事实地描写出来。据我所知，他从来没有提出过任何划分荣誉的百分比的事情，也没有说过佩雷尔曼应该和除我之外的任何其他人分享关于证明庞加莱猜想的荣誉。这当然是容易理解的，因为没有人比佩雷尔曼更加慷慨地承认我的工作。所谓丘窃取佩雷尔曼成就的说法远非事实，相反，丘一直称赞佩雷尔曼的工作，并和我一起支持他获得菲尔茨奖。事实上，没有谁比丘更应该为瑞奇流纲领的创建负责，而佩雷尔曼正是用它获得了这个（菲尔茨）奖。

您的忠诚的
理查德·汉密尔顿
哥伦比亚大学数学教授