Antoine Song
Antoine Song (born 18 July 1992 in Paris) is a French[1] mathematician whose research concerns differential geometry. In 2018, he proved Yau's conjecture. He is a Clay Research Fellow (2019–2024).[2] He obtained his Ph.D. from Princeton University in 2019 under the supervision of Fernando Codá Marques.[3]
Existence of minimal surfaces[]
It is known that any closed surface possesses infinitely many closed geodesics. The first problem in the minimal submanifolds section of Yau's list asks whether any closed three-manifold has infinitely many closed smooth immersed minimal surfaces. At the time it was known from Almgren–Pitts min-max theory the existence of at least one minimal surface. Kei Irie, Fernando Codá Marques, and André Neves solved this problem in the generic case [4] and later Antoine Song claimed it in full generality.[5]
Selected publications[]
- "Existence of infinitely many minimal hypersurfaces in closed manifolds"
References[]
- ^ Song's CV
- ^ "Antoine Song | Clay Mathematics Institute". www.claymath.org.
- ^ Antoine Song at the Mathematics Genealogy Project
- ^ "Density of minimal hypersurfaces for generic metrics | Annals of Mathematics".
- ^ Song, Antoine (2018). "Existence of infinitely many minimal hypersurfaces in closed manifolds". arXiv:1806.08816 [math.DG].
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- Living people
- Differential geometers
- Princeton University alumni
- 1992 births
- Scientists from Paris
- French mathematicians
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