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Existence of infinitely many minimal hypersurfaces in closed manifolds

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arxiv 1806.08816 v2 pith:CNKKMAOI submitted 2018-06-22 math.DG math.APmath.GT

Antoine Song This is my paper · ORCID
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keywords closedhypersurfacesinfinitelymanyminimalbuildsconjecturedeveloped
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Using min-max theory, we show that in any closed Riemannian manifold of dimension at least 3 and at most 7, there exist infinitely many smoothly embedded closed minimal hypersurfaces. It proves a conjecture of S.-T. Yau. This paper builds on the methods developed by F. C. Marques and A. Neves.

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  1. The p-widths of $RP^2$

    math.DG 2025-01 conditional novelty 6.0 of 10

    The p-widths of (RP^2, g_std) are ω_p = 2π floor((1+sqrt(1+8p))/4), achieved by Z2-invariant polynomial sweepouts.

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