Ricci curvature and minimal hypersurfaces with large Betti numbers

Puntos clave

• The aim is to construct Riemannian manifolds exhibiting positive Ricci curvature and analyze the properties of embedded minimal hypersurfaces.
• Construct closed (n+1)-dimensional Riemannian manifolds with positive Ricci curvature.
• Investigate embedded two-sided minimal hypersurfaces within these manifolds.
• Analyze the Morse index of hypersurfaces and their Betti numbers along a sequence.
• Each embedded minimal hypersurface has a Morse index of one.
• The first Betti numbers of the hypersurfaces are not uniformly bounded as the sequence progresses.

Resumen