Embedded minimal tori in \(S^3\) and the Lawson conjecture (Q392787)

The paper gives an affirmative answer to a well-known conjecture made by Lawson in 1970, which states that any embedded minimal torus in \(S^3\) is congruent to the Clifford torus. Here, the embeddedness assumption is essential as an infinite family of minimal immersions from a torus into \(S^3\) has been found by \textit{H. B. Lawson jun.} [Ann. Math. (2) 92, 335--374 (1970; Zbl 0205.52001)]. The key ingredient of the proof is a creative application of the maximum principle to a function defined on the space of pairs of points, a technique that was first used by \textit{G. Huisken} [Asian J. Math. 2, No. 1, 127--133 (1998; Zbl 0931.53032)] on his pioneering work on the curve-shortening flow.