In mathematics, Lawson's conjecture states that the Clifford torus is the only minimally embedded torus in the 3-sphereS3.[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
^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.
^Lawson, H. Blaine, Jr. (1970). "Complete minimal surfaces in S3". Ann. of Math.92 (3): 335–374. doi:10.2307/1970625. JSTOR 1970625.
^Norbury, Paul (2005). "The 12th problem" (PDF). The Australian Mathematical Society Gazette. 32 (4): 244–246.
^Brendle, Simon (2013). "Embedded minimal tori in S3 and the Lawson conjecture". Acta Mathematica. 211 (2): 177–190. doi:10.1007/s11511-013-0101-2. S2CID 119317563.
hsiang, lawson, conjecture, mathematics, lawson, conjecture, states, that, clifford, torus, only, minimally, embedded, torus, sphere, conjecture, featured, australian, mathematical, society, gazette, part, millennium, problems, series, march, 2012, simon, bren. 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 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 Lawson H Blaine Jr 1970 Complete minimal surfaces in S3 Ann of Math 92 3 335 374 doi 10 2307 1970625 JSTOR 1970625 Norbury Paul 2005 The 12th problem PDF The Australian Mathematical Society Gazette 32 4 244 246 Brendle Simon 2013 Embedded minimal tori in S3 and the Lawson conjecture Acta Mathematica 211 2 177 190 doi 10 1007 s11511 013 0101 2 S2CID 119317563 This differential geometry related article is a stub You can help Wikipedia by expanding it vte This topology related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Hsiang Lawson 27s conjecture amp oldid 1068177031, wikipedia, wiki, book, books, library,
