I try to interpret the ad in this way: Jerry Seinfeld is Mac, Bill represents Microsoft. Mac is more knowledgeable, and Microsoft learned from Mac (see how Bill learned to bend the shoe as Jerry), but in the end, they walked out together, and Jerry asked that cool question (typical Mac), which means Mac not practical? Bill was quite down to earth, and warm -- Microsoft is not evil? Mac found Microsoft, gave the advice, and followed Microsoft out, without getting paid... Vista is like that pair of shoes, they didn't fit well at the beginning, but if you bend it, work on it, it eventually will fit in just fine... Ha Ha!
Howard M Cooper Todd & Weld LLP 28 State Street, Boston, MA 02109 Direct Dial (617) 624-4713 / Fax (617) 227-5777 hcooper@toddweld.com
September 25, 2006
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 noncollapsing 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 fo
Prof. Richard Hamilton, Columbia Univ., responds to the New Yorker article, September 25, 2006
http://doctoryau.com/hamiltonletter.pdf
Howard M Cooper
Todd & Weld LLP
28 State Street, Boston, MA 02109
Direct Dial (617) 624-4713 / Fax (617) 227-5777
hcooper@toddweld.com
September 25, 2006
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 noncollapsing 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
Slashdot Mirror
I try to interpret the ad in this way: Jerry Seinfeld is Mac, Bill represents Microsoft. Mac is more knowledgeable, and Microsoft learned from Mac (see how Bill learned to bend the shoe as Jerry), but in the end, they walked out together, and Jerry asked that cool question (typical Mac), which means Mac not practical? Bill was quite down to earth, and warm -- Microsoft is not evil? Mac found Microsoft, gave the advice, and followed Microsoft out, without getting paid ... Vista is like that pair of shoes, they didn't fit well at the beginning, but if you bend it, work on it, it eventually will fit in just fine ... Ha Ha!
Prof. Richard Hamilton, Columbia Univ., responds to the New Yorker article, September 25, 2006
,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.
http://doctoryau.com/hamiltonletter.pdf
Howard M Cooper
Todd & Weld LLP
28 State Street, Boston, MA 02109
Direct Dial (617) 624-4713 / Fax (617) 227-5777
hcooper@toddweld.com
September 25, 2006
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
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 noncollapsing 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 fo
Prof. Richard Hamilton, Columbia Univ., responds to the New Yorker article, September 25, 2006 http://doctoryau.com/hamiltonletter.pdf Howard M Cooper Todd & Weld LLP 28 State Street, Boston, MA 02109 Direct Dial (617) 624-4713 / Fax (617) 227-5777 hcooper@toddweld.com September 25, 2006 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 noncollapsing 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