Connected sum of manifolds with spectral Ricci lower bounds

2025/05/23 by Gioacchino Antonelli, Kai Xu, Antonelli, Gioacchino +1
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2505.18320

openalex publication_date 2025/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let n > 2, γ> (n-1)/(n-2), and λ∈ ℝ. We prove that if M and N are two smooth n-manifolds that admit a complete Riemannian metric satisfying -γΔ+ Ric gt; λ,then the connected sum M # N also admits such a metric. The construction geometrically resembles a Gromov-Lawson tunnel; the range γ> (n-1)/(n-2) is sharp for this to hold.

Citations

• Proper solutions of the 1/H-flow and the Green kernel of the p-Laplacian
• Criticality, splitting theorems under spectral Ricci bounds and the topology of stable minimal hypersurfaces
• A sharp spectral splitting theorem
• New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry
• Four Lectures on Scalar Curvature
• A sphere theorem for three dimensional manifolds with integral pinched curvature

Related

• Positive scalar curvature metrics and aspherical summands
• Intermediate curvatures and highly connected manifolds
• Positive scalar curvature and connected sums
• Manifolds with A Lower Ricci Curvature Bound
• Positive intermediate Ricci curvature on connected sums