Remarks on minimal hypersurfaces in gradient shrinking Ricci solitons

2025/04/04 by Sun, Yukai, Zhu, Guangrui
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.03316

Abstract

In this paper, we prove that any compact 2-sided smooth stable minimal hypersurface in gradient Ricci soliton (Mⁿ,g,f) with scalar curvature R≥(n-1)λ must have vanished second fundamental form and vanished normal Ricci curvature. For shrinking gradient Ricci solitons with scalar curvature R≥(n-1)λ, the existence of an area-minimizing hypersurface would imply M is splitting.

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