Existence of Infinitely Many Minimal Hypersurfaces in Higher-dimensional Closed Manifolds with Generic Metrics

2019/01/24 by Li, Yangyang · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1901.08440

Abstract

In this paper, we show that a closed manifold Mⁿ⁺¹ (n ≥ 7) endowed with a C^∞-generic (Baire sense) metric contains infinitely many singular minimal hypersurfaces with optimal regularity. Moreover, for 2 ≤ n ≤ 6, our argument also implies the denseness of the minimal hypersurfaces realizing min-max widths for generic metrics. This partially supports equidistribution of the minimal hypersurfaces realizing min-max widths conjectured by F.C. Marques, A. Neves and A. Song.

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