Hsiang–Lawson's_conjecture

Hsiang–Lawson's conjecture

Hsiang–Lawson's conjecture

Theorem that the Clifford torus is the only minimally embedded torus in the 3-sphere

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

  1. [1]
    Lawson, H. Blaine Jr. (1970). "The unknottedness of minimal embeddings". Invent. Math. 11 (3): 183–187. Bibcode:1970InMat..11..183L. doi:10.1007/BF01404649. S2CID 122740925.
  2. [2]
    Lawson, H. Blaine Jr. (1970). "Complete minimal surfaces in S3". Ann. of Math. 92 (3): 335–374. doi:10.2307/1970625. JSTOR 1970625.
  3. [3]
    Norbury, Paul (2005). "The 12th problem" (PDF). The Australian Mathematical Society Gazette. 32 (4): 244–246.
  4. [4]
    Brendle, Simon (2013). "Embedded minimal tori in S3 and the Lawson conjecture". Acta Mathematica. 211 (2): 177–190. arXiv:1203.6597. doi:10.1007/s11511-013-0101-2. S2CID 119317563.


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