Presented by: 
Haizhong Li (Tsinghua / ANU)
Mon 24 Aug, 2:00 pm - 3:00 pm
Steele Building (03), room 262

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 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 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 or S^1(1/2)\times S^1(\sqrt{3}/2). For other values of the mean curvature, there exists embedded torus which is not S^1(r)\times S^1(\sqrt{1-r^2}). As a Corollary, our Theorem have solved the famous Pinkall-Sterling conjecture.