Differential geometry originated in17th century, and mainly used calculus to study the geometric properties of space, which greatly promoted physics, astronomy, engineering and so on. ? Ricky traffic? Born in 1980s, it is a research tool of differential geometry to describe spatial evolution.
From the expansion of the universe to the expansion of heat and contraction of cold, many natural phenomena can be attributed to spatial evolution. ? Professor Wang Bing said metaphorically, for example, if we blow a balloon, it will keep expanding, so it can be used? Ricky traffic? To study its spatial changes and finally get one? Perfect? The ideal result.
Chen Xiuxiong and Bing Wang have been studying differential geometry for a long time. Ricky traffic? Using new ideas and methods, they took the lead in proving? Hamilton-Tian? And then what? Partial zero-order estimation? These two core conjectures that have puzzled the mathematics field for more than 20 years.
It is understood that their research took five years, and the length of the paper exceeded 120 pages. Bing Wang said, like writing a novel? The difference is that it is driven by logic rather than stories. ?
It is worth mentioning that due to the voluminous space and long review period, it took another six years for this paper to be submitted and officially published. However, such a long publishing cycle is not uncommon in mathematics, because reviewers need enough time to understand new concepts and methods.
The reviewer of the Journal of Differential Geometry commented that this paper is a great progress in the field of geometric analysis and will stimulate many related studies. Fields Prize winner Simon? Donaldson praised, what is this? A major breakthrough in geometry in recent years? .
Before this paper was published, Bing Wang was just a? Plain? Geometry researcher. The encounter with teacher Chen Xiuxiong in 2003 opened the door for him to live in Ritchie.
What is Richie Stream? According to the definition, Ricci flow uses calculus to describe spatial evolution. Wang Bing explained this with soap bubbles? Description? :? Blowing a soap bubble may be dumbbell-shaped at first, but after floating in the air for a period of time, the shape will change slowly until it becomes a ball and no longer evolves. This? Ball? Is the steady state of bubbles. ? What is the function of Xiaoqiliu to study? Soap bubbles? Spatial change, and finally get one? Stable? The ideal result.
In 2003, Russian perelman claimed that he had solved the Poincare conjecture, which was based on the Ricci flow method. This made him have no doubt aboutNo. 1 in the study of Ricci flow at that time. However, this solution to differential geometry? A hundred years of unsolved cases? Bing Wang, who just went to the United States for postgraduate study, caught his epoch-making achievements? Handle? .
In the process of studying perelman's thesis, Bing Wang felt that he couldn't get out of it. After repeated thinking, Wang Bing had a bold guess: perelman was wrong.
Young graduate students want to give academic cows? Wrong choice? , specially wrote an email. To Bing Wang's surprise, this letter? Error correction sticker? Within three days, I got a reply from perelman. Academic Daniel admitted his mistakes in writing, and was surprised that no one pointed them out to him, although the article has been widely circulated for more than two years.
This time? Communication? Perelman's affirmation made Bing Wang more interested in Liu Liqi, and he also looked forward to more academic interaction with perelman.
Perelman didn't give Bing Wang this chance. After solving Poincare conjecture, perelman? See through the world of mortals? , directly out of mathematics. This makes the related research come to a standstill. And the tutor Chen Xiuxiong told Bing Wang: Good mathematics must have strong vitality, and perelman's mathematics must follow. Should we find a suitable starting point to continue digging? .
Perelman once mentioned in his article that his method can be used to study Kellogg flow. Perelman plans to solve Hamilton-Tian conjecture in his own way.
Although perelman's retirement makes this? Planning? It has become a distant future, but the future of Hamilton-Tian guess has been seen by Chen Xiuxiong. Combining Ritchie flow with Keller geometry to solve the complex two-dimensional Hamilton-Tian conjecture will become the focus of Chen Xiuxiong and Bing Wang in the next five years.
At the end of 20 13, Chen Xiuxiong and Bing Wang finally sorted out the idea of proof, and then spent half a year sorting out the contents. In the summer of 20 14, this certificate, which embodies the research results of five years and is signed by master and apprentice, was published on the pre-printed website arXiv. In this article on page 120, the master and the apprentice use self-designed auxiliary tools to solve the problem of space tension in Hamilton-Tian conjecture. Is it convenient? Part of the zero-order estimation conjecture proposed by 1990 is solved.