GTA Seminar: Li -- Embedded Constant Mean Curvature Tori in the Three-Sphere

Speaker: Prof. Haizhong Li (Tsinghua)

http://faculty.math.tsinghua.edu.cn/~hli/

Time: Friday, Feb. 7, 12NOON--1PM

Room: AGR (Carslaw 829)

Lunch: after the talk, at Law Annex Cafe. 

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Title: Embedded Constant Mean Curvature Tori in the Three-Sphere   


Abstract: this a joint work with Ben Andrews. The minimal surface 
is the surface with constant mean curvature zero. It was conjectured 
by H. B. Lawson in 1970s that the only embedded minimal torus in 
three-sphere is the Clifford torus. In 1980s, U. Pinkall and 
I. Sterling conjectured that embedded tori with CMC in three-sphere 
are surfaces of revolution. At March of 2012, Simon Brendle of 
Stanford University solved the Lawson conjecture. At April of 2012, 
Ben Andrews and Haizhong Li gave a complete classification of CMC 
embedded tori in the three-sphere. When the constant mean curvature 
is equal to zero or ±1 / \sqrt{3}, the only embedded torus is the 
Clifford torus. For other values of the mean curvature, there exists 
embedded torus which is not the Clifford torus, Ben Andrews and 
Haizhong Li gave a complete description of such surfaces. As a 
Corollary, Ben Andrews and Haizhong Li Theorem have solved the 
famous Pinkall-Sterling conjecture.

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Seminar website:

http://www.maths.usyd.edu.au/u/SemConf/Geometry/