Embedded constant mean curvature tori in the three-sphere
主 题: Embedded constant mean curvature tori in the three-sphere
报告人: Professor Haizhong Li (Tsinghua University)
时 间: 2014-10-31 15:00-16:00
地 点: 理科一号楼 1114（数学所活动）
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 Cli?ord torus. In 2012, Simon Brendle solved the Lawson conjecture by use of ”non-collapsing technique”. In 1980s, U. Pinkall and I. Sterling conjectured that embedded tori with CMC in three-sphere are surfaces of revolution. In 2012, Ben Andrews and I gave a complete classi?cation of CMC embedded tori in the three-sphere. When the con- stant mean curvature is equal to zero or ±1/√3, the only embedded torus is the Cli?ord torus or S1(1 2)×S1( √3 2 ). For other values of the mean cur- vature, there exists embedded torus which is not S1(r)×S1(√1?r2). As a Corollary, our Theorem have solved the famous Pinkall-Sterling conjecture.