| 词条 | Yau's conjecture |
| 释义 |
In differential geometry, Yau's conjecture from 1982, named after Shing-Tung Yau, is a mathematical conjecture which then states that a closed Riemannian three-manifold has an infinite number of smooth closed immersed minimal surfaces. It was the first problem in the Minimal submanifolds section in Yau's list of open problems. The conjecture has recently been claimed by Kei Irie, Fernando Codá Marques and André Neves in the generic case,[1][2] and by Antoine Song in full generality.[3] References1. ^{{cite arXiv |last1=Irie |first1=Kei |last2=Marques |first2=Fernando Codá |authorlink2=Fernando Codá Marques |last3=Neves |first3=André |authorlink3=André Neves |eprint=1710.10752 |title=Density of minimal hypersurfaces for generic metrics |class=math.DG |date=2017 }} 2. ^{{cite web|author=Carlos Matheus|url=https://matheuscmss.wordpress.com/2017/11/05/yaus-conjecture-of-abundance-of-minimal-hypersurfaces-is-generically-true-in-low-dimensions/|title=Yau’s conjecture of abundance of minimal hypersurfaces is generically true (in low dimensions) |date=November 5, 2017 }} 3. ^{{cite arXiv |last1=Song |first1=Antoine |eprint=1806.08816 |title=Existence of infinitely many minimal hypersurfaces in closed manifolds |class=math.DG |date=2018 }} Further reading
2 : Conjectures|Differential geometry |
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