Yau's conjecture
From HandWiki
In differential geometry, Yau's conjecture is a mathematical conjecture which states that any closed Riemannian 3-manifold has an infinite number of smooth closed immersed minimal surfaces. It is named after Shing-Tung Yau, who posed it as the 88th entry in his 1982 list of open problems in differential geometry.[1]
The conjecture was resolved by Kei Irie, Fernando Codá Marques and André Neves in the generic case,[2] and by Antoine Song in full generality.[3]
References
- ↑ Yau, Shing Tung (1982). "Problem section". Seminar on Differential Geometry. Annals of Mathematics Studies. 102. Princeton, NJ: Princeton University Press. pp. 669–706. doi:10.1515/9781400881918-035. ISBN 978-1-4008-8191-8.
- ↑ Irie, Kei; Marques, Fernando C.; Neves, André (2018). "Density of minimal hypersurfaces for generic metrics". Annals of Mathematics 187 (3): 963–972. doi:10.4007/annals.2018.187.3.8.
- ↑ Song, Antoine (2023). "Existence of infinitely many minimal hypersurfaces in closed manifolds". Annals of Mathematics 197 (3): 859–895. doi:10.4007/annals.2023.197.3.1.
External links
Carlos Matheus (November 5, 2017). "Yau's conjecture of abundance of minimal hypersurfaces is generically true (in low dimensions)". https://matheuscmss.wordpress.com/2017/11/05/yaus-conjecture-of-abundance-of-minimal-hypersurfaces-is-generically-true-in-low-dimensions/.
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