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Hsiang–Lawson's conjecture

In mathematics, Lawson's conjecture states that the Clifford torus is the only minimally embedded torus in the 3-sphere S3.[1][2] The conjecture was featured by the Australian Mathematical Society Gazette as part of the Millennium Problems series.[3]

In March 2012, Simon Brendle gave a proof of this conjecture, based on maximum principle techniques.[4]


  1. ^ Lawson, H. Blaine, Jr. (1970). "The unknottedness of minimal embeddings". Invent. Math. 11 (3): 183–187. doi:10.1007/BF01404649.
  2. ^ Lawson, H. Blaine, Jr. (1970). "Complete minimal surfaces in S3". Ann. of Math. 92 (3): 335–374. JSTOR 1970625.
  3. ^ Norbury, Paul (2005). "The 12th problem" (PDF). The Australian Mathematical Society Gazette. 32 (4): 244–246.
  4. ^ Brendle, Simon (2013). "Embedded minimal tori in S3 and the Lawson conjecture". Acta Mathematica. 211: 177–190. doi:10.1007/s11511-013-0101-2.