Remarks on minimal hypersurfaces in shrinking gradient Ricci solitons

In this paper, we prove that any compact 2-sided smooth stable minimal hypersurface in a shrinking 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 that M is splitting.