Hsiang–Lawson's conjecture

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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]

References[edit]

  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". 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.