His awards and honors include: In 1982, Richard S. Hamilton introduced the Ricci flow, proving a dramatic new theorem on the geometry of three-dimensional manifolds.
In his Ph.D. thesis, published in 1985, he showed that Yau's estimates in the resolution of the Calabi conjecture could be modified to the Kähler-Ricci flow context, to prove a convergence theorem similar to Hamilton's original result.
Following a suggestion of Yau's that the Ricci flow could be used to prove William Thurston's Geometrization conjecture, Hamilton developed the theory over the following two decades.
[3][4] Additionally, he posted a third article in which he gave a shortcut to the proof of the famous Poincaré conjecture, for which the results in the second half of the second paper were unnecessary.
[5] Perelman's papers were immediately recognized as giving notable new results in the theory of Ricci flow, although many mathematicians were unable to fully understand the technical details of some unusually complex or terse sections in his work.
[6] Cao collaborated with Xi-Ping Zhu of Zhongshan University, publishing an exposition in 2006 of Hamilton's work and of Perelman's first two papers, explaining them in the context of the mathematical literature on geometric analysis.
[7][8] The abstract of Cao and Zhu's article states In this paper, we give a complete proof of the Poincaré and the geometrization conjectures.
While the complete work is an accumulated efforts of many geometric analysts, the major contributors are unquestionably Hamilton and Perelman.Some observers felt that Cao and Zhu were overstating the value of their paper.