Ricci curvature and minimal hypersurfaces with large Betti numbers

Key Points

• These Riemannian manifolds can have embedded minimal hypersurfaces with Morse index one, ensuring stability.
• The first Betti numbers of the minimal hypersurfaces are not uniformly bounded as the manifolds evolve.
• This work provides a sequence of closed $(n+1)$-dimensional manifolds, enhancing the field of geometric analysis.
• Understanding these structures yields insights into the relationship between geometry and topology in higher dimensions.