Connected sum of manifolds with spectral Ricci lower bounds

Key Points

• The connected sum of two smooth n-manifolds can admit a complete Riemannian metric with spectral Ricci lower bounds.
• If both manifolds satisfy the inequality involving the Ricci tensor and Laplacian operator, their connection also satisfies it.
• The range for gamma is established as sharp, indicating a necessary condition for the result to hold.
• The construction is geometrically similar to a Gromov-Lawson tunnel, which illustrates the relationship between the manifolds.